BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mariya Soskova (University of Wisconsin) DTSTART:20200423T180000Z DTEND:20200423T190000Z DTSTAMP:20260422T225801Z UID:OLS/1 DESCRIPTION:Title: Frag ments of the Theory of Enumeration Degrees\nby Mariya Soskova (Univers ity of Wisconsin) as part of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/OLS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Margaret Thomas (Purdue) DTSTART:20200430T180000Z DTEND:20200430T190000Z DTSTAMP:20260422T225801Z UID:OLS/2 DESCRIPTION:Title: Poin t counting and parameterizations\nby Margaret Thomas (Purdue) as part of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/OLS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Rebecca Coulson (US Military Academy) DTSTART:20200507T180000Z DTEND:20200507T190000Z DTSTAMP:20260422T225801Z UID:OLS/3 DESCRIPTION:Title: The Bipartite Diameter 3 Metrically Homogeneous Graphs of Generic Type: Their Ages and Their Almost Sure Theories\nby Rebecca Coulson (US Military A cademy) as part of Online logic seminar\n\n\nAbstract\nFor the past 40 yea rs computer scientists generally believed that\nNP-complete problems are i ntractable. In particular\, Boolean\nsatisfiability (SAT)\, as a paradigma tic automated-reasoning problem\, has\nbeen considered to be intractable. Over the past 20 years\, however\, there\nhas been a quiet\, but dramatic\ , revolution\, and very large SAT instances\nare now being solved routinel y as part of software and hardware design.\nIn this talk I will review thi s amazing development and show how automated\nreasoning is now an industri al reality.\n\nI will then describe how we can leverage SAT solving to acc omplish\nother automated-reasoning tasks. Sampling uniformly at random sa tisfying\ntruth assignments of a given Boolean formula or counting the num ber of such\nassignments are both fundamental computational problems in co mputer\nscience with applications in software testing\, software synthesis \, machine\nlearning\, personalized learning\, and more. While the theory of these\nproblems has been thoroughly investigated since the 1980s\, app roximation\nalgorithms developed by theoreticians do not scale up to indus trial-sized\ninstances. Algorithms used by the industry offer better scal ability\,\nbut give up certain correctness guarantees to achieve scalabili ty. We\ndescribe a novel approach\, based on universal hashing and Satisfi ability\nModulo Theory\, that scales to formulas with hundreds of thousand s of\nvariables without giving up correctness guarantees.\n LOCATION:https://researchseminars.org/talk/OLS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Porter (Drake University) DTSTART:20200514T180000Z DTEND:20200514T190000Z DTSTAMP:20260422T225801Z UID:OLS/4 DESCRIPTION:Title: Rand omness extraction from a computability-theoretic perspective\nby Chris Porter (Drake University) as part of Online logic seminar\n\n\nAbstract\n The goal of this talk is to discuss recent work\, joint with Doug Cenzer\, on a notion of the extraction rate of Turing functionals that translate b etween notions of randomness with respect to different underlying probabil ity measures. We will analyze several classes of extraction procedures: a first that generalizes von Neumann's trick for extracting unbiased rando mness from the tosses of a biased coin\, a second based on work of generat ing biased randomness from unbiased randomness by Knuth and Yao\, and a th ird independently developed by Levin and Kautz that generalizes the data c ompression technique of arithmetic coding. For each of the above classes of extraction procedures\, we will identify a level of algorithmic randomn ess for an input that guarantees that we attain the corresponding extracti on rate in producing an output. I will aim to present this material in a way that is accessible to logicians who are not specialists in computabili ty theory / algorithmic randomness.\n LOCATION:https://researchseminars.org/talk/OLS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Moshe Vardi (Rice University) DTSTART:20200521T180000Z DTEND:20200521T190000Z DTSTAMP:20260422T225801Z UID:OLS/5 DESCRIPTION:Title: The automated-reasoning revolution: From theory to practice and back\nby M oshe Vardi (Rice University) as part of Online logic seminar\n\n\nAbstract \nFor the past 40 years computer scientists generally believed that\nNP-co mplete problems are intractable. In particular\, Boolean\nsatisfiability ( SAT)\, as a paradigmatic automated-reasoning problem\, has\nbeen considere d to be intractable. Over the past 20 years\, however\, there\nhas been a quiet\, but dramatic\, revolution\, and very large SAT instances\nare now being solved routinely as part of software and hardware design.\nIn this t alk I will review this amazing development and show how automated\nreasoni ng is now an industrial reality.\n\nI will then describe how we can levera ge SAT solving to accomplish\nother automated-reasoning tasks. Sampling u niformly at random satisfying\ntruth assignments of a given Boolean formul a or counting the number of such\nassignments are both fundamental computa tional problems in computer\nscience with applications in software testing \, software synthesis\, machine\nlearning\, personalized learning\, and mo re. While the theory of these\nproblems has been thoroughly investigated since the 1980s\, approximation\nalgorithms developed by theoreticians do not scale up to industrial-sized\ninstances. Algorithms used by the indus try offer better scalability\,\nbut give up certain correctness guarantees to achieve scalability. We\ndescribe a novel approach\, based on universa l hashing and Satisfiability\nModulo Theory\, that scales to formulas with hundreds of thousands of\nvariables without giving up correctness guarant ees.\n LOCATION:https://researchseminars.org/talk/OLS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Wesley Holliday (UC Berkeley) DTSTART:20200528T180000Z DTEND:20200528T190000Z DTSTAMP:20260422T225801Z UID:OLS/6 DESCRIPTION:Title: Exte nsions of choice-free Stone duality\nby Wesley Holliday (UC Berkeley) as part of Online logic seminar\n\n\nAbstract\nIn a recent paper\, “Choi ce-free Stone duality” (JSL\, March 2020)\, Nick Bezhanishvili and I dev eloped a choice-free duality theory for Boolean algebras using special spe ctral spaces\, called upper Vietoris spaces (UV-spaces). In this talk\, I will cover the basics of this duality and discuss some connections to othe r areas of logic.\n LOCATION:https://researchseminars.org/talk/OLS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:William Brian (UNC Charlotte) DTSTART:20200604T180000Z DTEND:20200604T190000Z DTSTAMP:20260422T225801Z UID:OLS/7 DESCRIPTION:Title: Limi ted-information strategies in Banach-Mazur games\nby William Brian (UN C Charlotte) as part of Online logic seminar\n\n\nAbstract\nThe Banach-Maz ur game is an infinite-length game played on a topological space X\, in wh ich two players take turns choosing members of an infinite decreasing sequ ence of open sets\, the first player trying to ensure that the intersectio n of this sequence is empty\, and the second that it is not. A limited-inf ormation strategy for one of the players is a game plan that\, on any give n move\, depends on only a small part of the game's history. In this talk we will discuss Telgársky's conjecture\, which asserts roughly that there must be topological spaces where winning strategies for the Banach Mazur game cannot be too limited\, but must rely on large parts of the game's hi story in a significant way. Recently\, it was shown that this conjecture f ails in models of set theory satisfying GCH + □. In such models it is al ways possible for one player to code all information concerning a game's h istory into a small piece of it. We will discuss these so-called coding st rategies\, why assuming GCH + □ makes them work so well\, and what can g o wrong in other models of set theory.\n LOCATION:https://researchseminars.org/talk/OLS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Samaria Montenegro Guzmán (U Costa Rica) DTSTART:20200611T180000Z DTEND:20200611T190000Z DTSTAMP:20260422T225801Z UID:OLS/8 DESCRIPTION:Title: Mode l Theory of Pseudo Real Closed Fields\nby Samaria Montenegro Guzmán ( U Costa Rica) as part of Online logic seminar\n\n\nAbstract\nThe notion of PAC field has been generalized by S. Basarab and by A. Prestel to ordered fields. Prestel calls a field M pseudo real closed (PRC) if M is existent ially closed in every regular extension L to which all orderings of M exte nd. Thus PRC fields are to real closed fields what PAC fields are to algeb raically closed fields.\nIn this talk we will study the class of pseudo re al closed fields (PRC-fields) from a model theoretical point of view and w e will explain some of the main results obtained. We know that the complet e theory of a bounded PRC field (i.e.\, with finitely many algebraic exten sions of degree m\, for each m > 1) is NTP_2 and we have a good descriptio n of forking.\n\nAlso\, in a joint work with Alf Onshuus and Pierre Simon we describe the definable groups in the case that they have f-generics typ es.\n\nIn the end of the talk we will explain some results obtained with S ilvain Rideau. Where we generalize the notion of PRC fields to a more gene ral class of fields. In particular\, this class includes fields that have orders and valuations at the same time.\n LOCATION:https://researchseminars.org/talk/OLS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Rodrigo Torres-Avilés (U Bio Bio) DTSTART:20200625T180000Z DTEND:20200625T190000Z DTSTAMP:20260422T225801Z UID:OLS/9 DESCRIPTION:Title: Topo logical Mixing and Linear Recurrence on SMART\nby Rodrigo Torres-Avil és (U Bio Bio) as part of Online logic seminar\n\n\nAbstract\nThe goal of this talk is to analize recent work on properties of the subshift derivat ed of a particular Turing machine\, nicknamed SMART\, which has a lot of i nteresting properties (as topological minimality and aperiodicity). First\ , we review a combinatorial proof of the Topological Mixing property of th e subshift derivated from SMART\, and later\, we deepen to tie general sub shift of Turing Machines with more general properties\, as linear recurren ce.\n LOCATION:https://researchseminars.org/talk/OLS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Towsner (U Penn) DTSTART:20200709T180000Z DTEND:20200709T190000Z DTSTAMP:20260422T225801Z UID:OLS/11 DESCRIPTION:Title: Sho uld we believe in nonstandard analysis?\nby Henry Towsner (U Penn) as part of Online logic seminar\n\n\nAbstract\nNonstandard analysis has been the one of the focal points for debate about the role of the axiom of choi ce in mathematics. I'll argue that this discussion often conflates two di stinct issues - the question of whether mathematical arguments are valid\, and the question of whether all mathematical objects should be understood to "exist" in the same way. I'll discuss various ways of showing that mo st uses of nonstandard analysis in mathematics don't actually use the axio m of choice\, and how this perspective can be used to obtain new mathemati cal results (including applications\, joint with William Simmons\, to find ing new bounds for primality testing in polynomial rings). On the other h and\, I'll argue (based on joint work with Kenny Easwaran) that the same p erspective argues against interpreting nonstandard values too literally wh en considering applications with real-world interpretations.\n LOCATION:https://researchseminars.org/talk/OLS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Elaine Pimentel (DMAT/UFRN) DTSTART:20200618T180000Z DTEND:20200618T190000Z DTSTAMP:20260422T225801Z UID:OLS/12 DESCRIPTION:Title: A g ame model for proofs with costs\nby Elaine Pimentel (DMAT/UFRN) as par t of Online logic seminar\n\n\nAbstract\nWe look at substructural calculi from a game semantic point of view\, guided by certain intuitions about re source conscious and\, more specifically\, cost conscious reasoning. To th is aim\, we start with a game\, where player I defends a claim correspondi ng to a (single-conclusion) sequent\, while player II tries to refute that claim. Branching rules for additive connectives are modeled by choices of II\, while branching for multiplicative connectives leads to splitting th e game into parallel subgames\, all of which have to be won by player I to succeed. The game comes into full swing by adding cost labels to assumpti ons\, and a corresponding budget. Different proofs of the same end-sequent are interpreted as more or less expensive strategies for \\I to defend th e corresponding claim. This leads to a new kind of labelled calculus\, whi ch can be seen as a fragment of SELL (subexponential linear logic). Final ly\, we generalize the concept of costs in proofs by using a semiring stru cture\, illustrate our interpretation by examples and investigate some pro of-theoretical properties.\nThis is a joint work with Timo Lang\, Carlos O larte and Christian G. Fermüller\n LOCATION:https://researchseminars.org/talk/OLS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Linda Brown Westrick (Penn State) DTSTART:20200716T180000Z DTEND:20200716T190000Z DTSTAMP:20260422T225801Z UID:OLS/13 DESCRIPTION:Title: Bor el combinatorics fail in HYP\nby Linda Brown Westrick (Penn State) as part of Online logic seminar\n\n\nAbstract\nWe show that the Borel Dual Ra msey Theorem fails in HYP\, regardless of the number of partitions k ≥ 2 . Therefore\, the Borel Dual Ramsey Theorem is not a statement of hyperari thmetic analysis. We also apply similar methods\, namely construction of c ompletely determined pseudo-Borel codes via decorating trees\, to obtain r esults concerning some theorems about Borel graph coloring and the prisone r hat problem. Joint work with Henry Towsner and Rose Weisshaar.\n LOCATION:https://researchseminars.org/talk/OLS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Dana Bartošová (U Florida) DTSTART:20200723T180000Z DTEND:20200723T190000Z DTSTAMP:20260422T225801Z UID:OLS/14 DESCRIPTION:Title: Dyn amics of finite products of groups and of group extensions\nby Dana Ba rtošová (U Florida) as part of Online logic seminar\n\n\nAbstract\nWe wi ll investigate how universal minimal flows interact with group operations. We show that the universal minimal flow of the product of two copies of i ntegers is far from the product of two copies of the universal minimal flo w of integers. On the other hand\, when a topological group is a group ext ension of a compact group by a discrete group\, then the universal minimal flow can be computed from the discrete and compact parts.\n LOCATION:https://researchseminars.org/talk/OLS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruiyuan Chen (U Illinois Urbana-Champaign) DTSTART:20200702T180000Z DTEND:20200702T190000Z DTSTAMP:20260422T225801Z UID:OLS/15 DESCRIPTION:Title: Sto ne duality and strong conceptual completeness for infinitary logic\nby Ruiyuan Chen (U Illinois Urbana-Champaign) as part of Online logic semina r\n\n\nAbstract\nThe classical Stone duality\, applied to the Lindenbaum-T arski\nalgebra of a propositional theory\, allows the syntax of the theory to be\ncanonically recovered from its space of models\; this encompasses both\nthe completeness and definability theorems for propositional logic.\ nMany known variants and generalizations of Stone duality have analogous\n interpretations as completeness-definability theorems for various\nfragmen ts of finitary propositional and first-order logic. In this\ntalk\, I wil l give an overview of this duality-theoretic approach to\ncompleteness\, i ncluding the key examples of Stone duality as well as\nMakkai duality for first-order logic. I will then present a duality\ntheorem for the countab ly infinitary first-order logic\n$L_{\\omega_1\\omega}$\, proved using too ls from invariant descriptive set\ntheory as well as topos theory.\n LOCATION:https://researchseminars.org/talk/OLS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuela Busaniche (CCT CONICET Santa Fe) DTSTART:20200730T180000Z DTEND:20200730T190000Z DTSTAMP:20260422T225801Z UID:OLS/16 DESCRIPTION:Title: Res iduated Lattices: algebraic constructions related to substructural logics< /a>\nby Manuela Busaniche (CCT CONICET Santa Fe) as part of Online logic s eminar\n\n\nAbstract\nSubstructural logics are logics that\, when they are formulated in a Gentzen style system\, they lack some of the structural r ules: contraction\, weakening or exchange.The importance of the theory of substructural logics relies on the fact that they provide a common framewo rk where different logical systems can be compared. They include intuition istic logic\, fuzzy logics\, relevance logics\, linear logic\, many-valued logics and others.\n\nTheir algebraic semantics are based on residuated l attices. The class of these ordered algebraic structures is quite big and hard to study\, but it contains some proper subclasses that are well-known such as Boolean algebras\, Heyting algebras\, MV-algebras. In this talk w e will see different constructions of new residuated lattices based on bet ter-known algebras.\n LOCATION:https://researchseminars.org/talk/OLS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:James Worrell (U of Oxford) DTSTART:20200806T180000Z DTEND:20200806T190000Z DTSTAMP:20260422T225801Z UID:OLS/17 DESCRIPTION:Title: Dec ision problems in program analysis\nby James Worrell (U of Oxford) as part of Online logic seminar\n\n\nAbstract\nWe consider decision problems for affine programs: a simple model from the field of program analysis. In this talk we focus on deciding the existence of algebraic and semi-algebr aic invariants that separate reachable from non-reachable program states\, and on deciding termination. We will survey some recently obtained decisi on procedures for these problems\, and highlight some longstanding open qu estions.\n LOCATION:https://researchseminars.org/talk/OLS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:James Hanson (U of Wisconsin) DTSTART:20200813T180000Z DTEND:20200813T190000Z DTSTAMP:20260422T225801Z UID:OLS/18 DESCRIPTION:Title: Str ongly Minimal Sets in Continuous Logic\nby James Hanson (U of Wisconsi n) as part of Online logic seminar\n\n\nAbstract\nContinuous logic is a ge neralization of first-order logic suited to studying structures with a rea l-valued metric. There is a natural generalization of the notion of strong ly minimal sets to continuous logic\, and\, while they do not play quite t he same role in characterizing theories categorical in uncountable cardina lities\, they are interesting in their own right. After developing some of the basic machinery of strongly minimal sets in continuous logic\, we wil l characterize the essentially continuous strongly minimal theories\, i.e. those which do not interpret an infinite discrete structure\, and we will leverage this into a precise characterization of the essentially continuo us strongly minimal groups.\n LOCATION:https://researchseminars.org/talk/OLS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Damir Dzhafarov (U of Connecticut) DTSTART:20200820T180000Z DTEND:20200820T190000Z DTSTAMP:20260422T225801Z UID:OLS/19 DESCRIPTION:Title: Mil liken's tree theorem and computability theory\nby Damir Dzhafarov (U o f Connecticut) as part of Online logic seminar\n\n\nAbstract\nMilliken's t ree theorem is a powerful combinatorial result that generalized Ramsey's t heorem and many other familiar partition results. I will present recent wo rk on the effective and proof-theoretic strength of this theorem\, which w as originally motivated by a question of Dobrinen. The main result is a co mplete characterization of Milliken's tree theorem in terms of reverse mat hematics and the usual computability-theoretic hierarchies\, along with se veral applications to other combinatorial problems. Key to this is a new i nductive proof of Milliken's tree theorem\, employing an effective version of the Halpern-Lauchli theorem. This is joint work with Angles d'Auriac\, Cholak\, Monin\, and Patey.\n LOCATION:https://researchseminars.org/talk/OLS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Mirna Džamonja (IHPST\, CNRS-Université Panthéon-Sorbonne Paris \, France) DTSTART:20200910T180000Z DTEND:20200910T190000Z DTSTAMP:20260422T225801Z UID:OLS/20 DESCRIPTION:Title: On logics that make a bridge from the Discrete to the Continuous\nby Mirn a Džamonja (IHPST\, CNRS-Université Panthéon-Sorbonne Paris\, France) a s part of Online logic seminar\n\n\nAbstract\nWe study logics which model the passage between an infinite sequence of finite models to an uncountabl e limiting object\, such as is the case in the context of graphons. Of par ticular interest is the connection between the countable and the uncountab le object that one obtains as the union versus the combinatorial limit of the same sequence.\n LOCATION:https://researchseminars.org/talk/OLS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Carl Mummert (Marshall University) DTSTART:20200903T180000Z DTEND:20200903T190000Z DTSTAMP:20260422T225801Z UID:OLS/21 DESCRIPTION:Title: The strength of König's edge coloring theorem\nby Carl Mummert (Marshall University) as part of Online logic seminar\n\n\nAbstract\nKönig's edge coloring theorem says that a bipartite graph with\nmaximal degree $n$ has an edge coloring with no more than $n$ colors.\nWe study the computability theory and Reverse Mathematics of this theorem. Computable bipartite grap hs with degree bounded by $n$ have computable edge colorings with $2n-1$ c olors\, but the theorem that there is an edge coloring with $n$ colors is equivalent to $\\mathsf{WKL}_0$ over $\\mathsf{RCA}_0$. The number of colo rs permitted affects the computability of the solution. We obtain an add itional proof of the following theorem of Paul Shafer: $\\mathsf{WKL}_0$ is equivalent over $\\mathsf{RCA}_0$ to the \nprinciple that a countable b ipartite n-regular graph is the union of n complete matchings.\n LOCATION:https://researchseminars.org/talk/OLS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Dima Sinapova (U Illinois Chicago) DTSTART:20200827T180000Z DTEND:20200827T190000Z DTSTAMP:20260422T225801Z UID:OLS/22 DESCRIPTION:Title: Ite ration\, reflection\, and Prikry forcing\nby Dima Sinapova (U Illinois Chicago) as part of Online logic seminar\n\n\nAbstract\nThere is an inher ent tension between stationary reflection and the failure of the singular cardinal hypothesis (SCH). The former is a compactness type principle that follows from large cardinals. Compactness is the phenomenon where if a ce rtain property holds for every smaller substructure of an object\, then it holds for the entire object. In contrast\, failure of SCH is an instance of incompactness. It is usually obtained using Prikry forcing.\n\nWe descr ibe a Prikry style iteration\, and use it to force stationary reflection i n the presence of not SCH. Then we discuss the situation at smaller cardin als. This is joint work with Alejandro Poveda and Assaf Rinot.\n LOCATION:https://researchseminars.org/talk/OLS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Berenstein (U de los Andes) DTSTART:20200917T180000Z DTEND:20200917T190000Z DTSTAMP:20260422T225801Z UID:OLS/23 DESCRIPTION:Title: Exp ansions of geometric theories as measurable structures\nby Alexander B erenstein (U de los Andes) as part of Online logic seminar\n\n\nAbstract\n We say that a theory T is geometric if for any model $M\\models T$ the alg ebraic closure satisfies the exchange property and T eliminates the quanti fier $\\exists^{\\infty}$. We will explain how to define\, inside a geomet ric theory\, a well behaved notion of dimension for definable sets. We wil l then consider the special case where the underlying theory is measurable (in the sense of Macpherson and Steinhorn) of SU-rk one\, where besides a dimension we can also assign a measure to definable sets. We will then in troduce an expansion called an H-structures and show that it can be studie d as a generalized measurable structure whose dimension has values in $\\o mega^2$. This is joint work with García and Zou.\n LOCATION:https://researchseminars.org/talk/OLS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Noquez (Indiana University) DTSTART:20201001T180000Z DTEND:20201001T190000Z DTSTAMP:20260422T225801Z UID:OLS/24 DESCRIPTION:Title: The Sierpinski Carpet as a Final Coalgebra Obtained by Completing an Initial Algebra\nby Victoria Noquez (Indiana University) as part of Online log ic seminar\n\n\nAbstract\nThe background for this work includes Freyd's Th eorem\, in which the unit interval is viewed as a final coalgebra of a cer tain endofunctor in the category of bipointed sets. Leinster generalized t his to a broad class of self-similar spaces in categories of sets\, also c haracterizing them as topological spaces. Bhattacharya\, Moss\, Ratnayake\ , and Rose went in a different direction\, working in categories of metric spaces\, obtaining the unit interval and the Sierpinski Gasket as a final colagebras in the categories of bipointed and tripointed metric spaces re spectively. To achieve this they used a Cauchy completion of an initial al gebra to obtain the required final coalgebra. In their examples\, the iter ations of the fractals can be viewed as gluing together a finite number of scaled copies of some set at some finite set of points (e.g. corners of t riangles). Here we will expand these ideas to apply to a broader class of fractals\, in which copies of some set are glued along segments (e.g. side s of a square). We use the method of completing an initial algebra to obta in the Sierpinski Carpet as a final coalgebra in a category of metric spac es\, and note the required adaptations to this approach\, most notably tha t we no longer get the initial algebra as the colimit of a countable seque nce of metric spaces. We will explore some ways in which these results may be further generalized to a broader class of fractals. Joint work with La rry Moss.\n LOCATION:https://researchseminars.org/talk/OLS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Anush Tserunyan (McGill University) DTSTART:20201119T190000Z DTEND:20201119T200000Z DTSTAMP:20260422T225801Z UID:OLS/25 DESCRIPTION:Title: Con tainers made easy\nby Anush Tserunyan (McGill University) as part of O nline logic seminar\n\n\nAbstract\nA modern trend in extremal combinatoric s is extending classical results from the dense setting (e.g. Szemer&eacut e\;di's theorem) to the sparse random setting. More precisely\, one shows that a property of a given ``dense'' structure is inherited by a randomly chosen ``sparse'' substructure. A recent breakthrough tool for proving suc h statements is the Balogh--Morris--Samotij and Saxton--Thomason hypergrap h containers method\, which bounds the number of independent sets in homog eneously dense finite hypergraphs\, thus implying that a random sparse sub set is not independent. In a joint work with A. Bernshteyn\, M. Delcourt\, and H. Towsner\, we give a new --- elementary and nonalgorithmic --- proo f of the containers theorem for finite hypergraphs. Our proof is inspired by considering hyperfinite hypergraphs in the setting of nonstandard analy sis\, where there is a notion of dimension capturing the logarithmic rate of growth of finite sets. Applying this intuition in another setting with a notion of dimension\, namely\, algebraically closed fields\, A. Bernshte yn\, M. Delcourt\, and I prove an analogous theorem for ``dense'' algebrai cally definable hypergraphs: any Zariski-generic low-dimensional subset of such hypergraphs is itself ``dense'' (in particular\, not independent).\n LOCATION:https://researchseminars.org/talk/OLS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Arno Pauly (Swansea University) DTSTART:20200924T180000Z DTEND:20200924T190000Z DTSTAMP:20260422T225801Z UID:OLS/27 DESCRIPTION:Title: How computability-theoretic degree structures and topological spaces are rela ted\nby Arno Pauly (Swansea University) as part of Online logic semina r\n\n\nAbstract\nWe can generalize Turing reducibility to points in a larg e class of topological spaces. The point degree spectrum of a space is the collection of the degrees of its points. This is always a collection of M edvedev degrees\, and it turns out that topological properties of the spac e are closely related to what degrees occur in it. For example\, a Polish space has only Turing degrees iff it is countably dimensional. This connec tion can be used to bring topological techniques to bear on problems from computability theory and vice versa. The talk is based on joint work with Takayuki Kihara and Keng Meng Ng (https://arxiv.org/abs/1405.6866 and http s://arxiv.org/abs/1904.04107).\n LOCATION:https://researchseminars.org/talk/OLS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Johanna Franklin (Hofstra University) DTSTART:20201203T190000Z DTEND:20201203T200000Z DTSTAMP:20260422T225801Z UID:OLS/28 DESCRIPTION:Title: Lim iting densities and finitely presented structures\nby Johanna Franklin (Hofstra University) as part of Online logic seminar\n\n\nAbstract\nWe ad dress the question of typicality for structures by studying the limiting d ensities of various properties. We define the limiting density of a proper ty Q to be the limit of the fraction of presentations of a variety with re lators of length at most s that have property Q as s goes to infinity. Aft er providing some initial examples\, we present a more general approach to our question. This work is joint with Meng-Che "Turbo" Ho and Julia Knigh t.\n LOCATION:https://researchseminars.org/talk/OLS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Angeliki Koutsoukou-Argyraki (U of Cambridge) DTSTART:20210121T190000Z DTEND:20210121T200000Z DTSTAMP:20260422T225801Z UID:OLS/29 DESCRIPTION:Title: Ari stotle's Assertoric Syllogistic in Isabelle/HOL\nby Angeliki Koutsouko u-Argyraki (U of Cambridge) as part of Online logic seminar\n\n\nAbstract\ nI discuss my formalisation of some basic elements of\nAristotle's asserto ric syllogistic\nusing the proof assistant (interactive theorem prover) Is abelle/HOL. The\nformal proof development can\nbe found on the Arch ive of Formal Proofs\n LOCATION:https://researchseminars.org/talk/OLS/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksandra Kwiatkowska (U of Wrocław) DTSTART:20210114T190000Z DTEND:20210114T200000Z DTSTAMP:20260422T225801Z UID:OLS/30 DESCRIPTION:Title: Sim plicity of the automorphism groups of countable homogeneous structures \nby Aleksandra Kwiatkowska (U of Wrocław) as part of Online logic semina r\n\n\nAbstract\nThe program of understanding the normal subgroup structur e of groups that arise as automorphism groups of countable structures date s back at least to the ’50s\, when Higman described all proper normal su bgroups of the automorphism group of rationals (Q\,<). In recent several y ears Tent-Ziegler\, following the work of Macpherson-Tent\, proved simplic ity for many automorphism groups of countable graphs and metric spaces. In the talk\, we prove simplicity for the automorphism groups of order and t ournament expansions of homogeneous structures such as the bounded Urysohn metric space and the random graph. In particular\, we show that the autom orphism group of the linearly ordered random graph is a simple group. This is joint work with Filippo Calderoni and Katrin Tent.\n LOCATION:https://researchseminars.org/talk/OLS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Steffen Lempp (U of Wisconsin) DTSTART:20201022T180000Z DTEND:20201022T190000Z DTSTAMP:20260422T225801Z UID:OLS/31 DESCRIPTION:Title: The Turing Degrees: On the Order Dimension of and Embeddings into the Turing Degrees\nby Steffen Lempp (U of Wisconsin) as part of Online logic sem inar\n\n\nAbstract\nIn joint work with Higuchi\, Raghavan and Stephan\, we show that the order dimension of any locally countable partial ordering ( P\, <) of size κ+\, for any κ of uncountable cofinality\, is at most κ. \nIn particular\, this implies that it is consistent with ZFC that the dim ension of the Turing degrees under partial ordering can be strictly less t han the continuum. (Kumar and Raghavan have since shown that it can also b e continuum\, thus the order dimension of the Turing degrees is independen t of ZFC.)\nThis is closely related to an old question of Sacks from 1963 about whether the Turing degrees form a universal locally countable partia l order of size continuum.\n LOCATION:https://researchseminars.org/talk/OLS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Lynn Scow (Cal State San Bernardino) DTSTART:20201112T190000Z DTEND:20201112T200000Z DTSTAMP:20260422T225801Z UID:OLS/32 DESCRIPTION:Title: Tra nsfer of the Ramsey property\nby Lynn Scow (Cal State San Bernardino) as part of Online logic seminar\n\n\nAbstract\nRamsey's theorem for finite sequences is a special case of a class of finite structures having the Ra msey property\, where that class is the age of $(\\mathbb{Q}\,<)$. Given two classes $\\mathcal{K}_1$\nand $\\mathcal{K}_2$\, each with the Ramsey property\, there are many lenses through which one might examine how the R amsey property transfers from $\\mathcal{K}_1$ to $\\mathcal{K}_2$. We wi ll present some approaches.\n LOCATION:https://researchseminars.org/talk/OLS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Přenosil (Vanderbilt University) DTSTART:20201029T180000Z DTEND:20201029T190000Z DTSTAMP:20260422T225801Z UID:OLS/33 DESCRIPTION:Title: Sem isimplicity\, Glivenko theorems\, and the excluded middle\nby Adam Př enosil (Vanderbilt University) as part of Online logic seminar\n\n\nAbstra ct\nThere are at least three different ways to obtain classical propositio nal logic from intuitionistic propositional logic. Firstly\, it is the ext ension of intuitionistic logic by the law of the excluded middle (LEM). Se condly\, it is related to intuitionistic logic by the double-negation tran slation of Glivenko. Finally\, the algebraic models of classical logic are precisely the semisimple algebraic models of intuitionistic logic (i.e. B oolean algebras are precisely the semisimple Heyting algebras). We show ho w to formulate the equivalence between the LEM and semisimplicity\, and be tween what we might call the Glivenko companion and the semisimple compani on of a logic\, at an appropriate level of generality. This equivalence wi ll subsume several existing Glivenko-like theorems\, as well as some new o nes. It also provides a useful technique for describing the semisimple sub varieties of a given variety of algebras. This is joint work with Tomáš Lávička\, building on previous work by James Raftery.\n LOCATION:https://researchseminars.org/talk/OLS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Cholak (University of Notre Dame) DTSTART:20210204T190000Z DTEND:20210204T200000Z DTSTAMP:20260422T225801Z UID:OLS/35 DESCRIPTION:Title: Old and new results on the computably enumerable sets\nby Peter Cholak (U niversity of Notre Dame) as part of Online logic seminar\n\n\nAbstract\nWe will survey a number of old results on the computably enumerable sets and finish with a few new results. The computably enumerable sets are intere sting since anything which can happen computably happens in computably enu merable sets.\n LOCATION:https://researchseminars.org/talk/OLS/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Farzaneh Derakhshan (Carnegie Mellon) DTSTART:20201105T190000Z DTEND:20201105T200000Z DTSTAMP:20260422T225801Z UID:OLS/36 DESCRIPTION:Title: Str ong Progress for Session-Typed Processes in a Linear Metalogic with Circul ar Proofs\nby Farzaneh Derakhshan (Carnegie Mellon) as part of Online logic seminar\n\n\nAbstract\nSession types describe the communication beha vior of interacting processes. Binary session types are a particular form of session types in which each channel has two endpoints. The strong progr ess property states that a recursive process either terminates or communic ates along one of its external channels after a finite number of steps. In this talk\, I show how to prove strong progress for valid session-typed p rocesses defined in an asynchronous computational semantics\, working in a fragment of binary session types in which a process can use at most one r esource. We formalize a proof of strong progress via a processes-as-formul as interpretation into a metalogic that we have introduced. The metalogic is an infinitary first order linear calculus with least and greatest fixed -points. We build a circular derivation for the strong progress property o f processes in this first order calculus. By enforcing a condition on the logical derivations\, we ensure their cut elimination property and soundne ss of the strong progress theorem.\n LOCATION:https://researchseminars.org/talk/OLS/36/ END:VEVENT BEGIN:VEVENT SUMMARY:John Baldwin (University of Illinois\, Chicago) DTSTART:20201015T180000Z DTEND:20201015T190000Z DTSTAMP:20260422T225801Z UID:OLS/37 DESCRIPTION:Title: Tow ards a finer classification of Strongly minimal sets\nby John Baldwin (University of Illinois\, Chicago) as part of Online logic seminar\n\n\nAb stract\nPDF Abstract posted on Seminar Web page at http://lagrange. math.siu.edu/calvert/OnlineSeminar/Baldwin201015ab.pdf\n LOCATION:https://researchseminars.org/talk/OLS/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Artem Chernikov (UCLA) DTSTART:20201008T180000Z DTEND:20201008T190000Z DTSTAMP:20260422T225801Z UID:OLS/38 DESCRIPTION:Title: Ide mpotent Keisler measures\nby Artem Chernikov (UCLA) as part of Online logic seminar\n\n\nAbstract\nIn model theory\, a type is an ultrafilter on the Boolean algebra of definable sets\, and is the same thing as a finite ly additive {0\,1}-valued measure. This is a special kind of a Keisler mea sure\, which is just a finitely additive real-valued probability measure o n the Boolean algebra of definable sets. If the structure we are consideri ng expands a group (i.e. the group operations are definable)\, it often li fts to a natural semigroup operation on the space of its types/measures\, and it makes sense to talk about the idempotent ones among them. For insta nce\, idempotent ultrafilters on the integers provide an elegant proof of Hindman's theorem\, and fit into this setting taking the structure to be ( Z\,+) with all of its subsets named by predicates. On the other hand\, in the context of locally compact abelian groups\, classical work by Wendel\, Rudin\, Cohen (before inventing forcing) and others classifies idempotent Borel measures\, showing that they are precisely the Haar measures of com pact subgroups. I will discuss recent joint work with Kyle Gannon aiming t o unify these two settings\, leading in particular to a classification of idempotent Keisler measures in stable theories.\n LOCATION:https://researchseminars.org/talk/OLS/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Gil Sagi (U of Haifa) DTSTART:20201210T190000Z DTEND:20201210T200000Z DTSTAMP:20260422T225801Z UID:OLS/39 DESCRIPTION:Title: For malization\, Commitments and Constraints\nby Gil Sagi (U of Haifa) as part of Online logic seminar\n\n\nAbstract\nThe topic of this talk is form alization: the assignment of formal language arguments to natural language arguments for the sake of evaluating the latter's validity. It has been r ecognized in the literature that formalization is far from a trivial proce ss. One must discern the logical from the nonlogical in the sentence\, a p rocess that requires theorizing that goes beyond the mere understanding of the sentence formalized (Brun 2014). Moreover\, according to some\, forma lization is a form of explication\, and it "involves creative and normativ e aspects of constructing logical forms" (ibid).\n\nIn previous work\, I p roposed a model-theoretic framework of "semantic constraints\," where ther e is no strict distinction between logical and nonlogical vocabulary. The form of sentences in a formal language is determined rather by a set of co nstraints on models. In the talk\, I will show how this framework can also be used in the process of formalization\, where the semantic constraints are conceived of as commitments made with respect to the language. I will extend the framework to include "formalization constraints" on functions t aking arguments from a source language to a target language\, and I will c onsider various meta-constraints on both the process of formalization and its end result.\n LOCATION:https://researchseminars.org/talk/OLS/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Raimundo Briceño (Pontificia Universidad Católica de Chile) DTSTART:20210128T190000Z DTEND:20210128T200000Z DTSTAMP:20260422T225801Z UID:OLS/40 DESCRIPTION:Title: Dis mantlability\, connectedness\, and mixing in relational structures\nby Raimundo Briceño (Pontificia Universidad Católica de Chile) as part of Online logic seminar\n\n\nAbstract\nThe Constraint Satisfaction Problem (C SP) and its counting counterpart appears under different guises in many ar eas of mathematics\, computer science\, and elsewhere. Its structural and algorithmic properties have demonstrated to play a crucial role in many of those applications. For instance\, in the decision CSPs\, structural prop erties of the relational structures involved —like\, for example\, disma ntlability— and their logical characterizations have been instrumental f or determining the complexity and other properties of the problem. Topolog ical properties of the solution set such as connectedness are related to t he hardness of CSPs over random structures. Additionally\, in approximate counting and statistical physics\, where CSPs emerge in the form of spin s ystems\, mixing properties and the uniqueness of Gibbs measures have been heavily exploited for approximating partition functions and free energy.\n \nIn spite of the great diversity of those features\, there are some eerie similarities between them. These were observed and made more precise in t he case of graph homomorphisms by Brightwell and Winkler\, who showed that dismantlability of the target graph\, connectedness of the set of homomor phisms\, and good mixing properties of the corresponding spin system are a ll equivalent. In this talk we go a step further and demonstrate similar c onnections for arbitrary CSPs. This requires a much deeper understanding o f dismantling and the structure of the solution space in the case of relat ional structures\, and also new refined concepts of mixing. In addition\, we develop properties related to the study of valid extensions of a given partially defined homomorphism\, an approach that turns out to be novel ev en in the graph case. We also add to the mix the combinatorial property of finite duality and its logic counterpart\, FO-definability\, studied by L arose\, Loten\, and Tardif. This is joint work with Andrei Bulatov\, Víct or Dalmau\, and Benoît Larose.\n LOCATION:https://researchseminars.org/talk/OLS/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcos Mazari-Armida (Carnegie Mellon University) DTSTART:20210218T190000Z DTEND:20210218T200000Z DTSTAMP:20260422T225801Z UID:OLS/41 DESCRIPTION:Title: Cha racterizing noetherian rings via superstability\nby Marcos Mazari-Armi da (Carnegie Mellon University) as part of Online logic seminar\n\n\nAbstr act\nWe will show how superstability of certain classes of modules can be used to characterize noetherian rings. None of the classes of modules that we will consider are axiomatizable by a complete first-order theory and s ome of them are not even first-order axiomatizable\, but they are all Abst ract Elementary Classes (AECs). This new way of looking at classes of modu les as AECs will be emphasized as I think it can have interesting applicat ions. If time permits we will see how the ideas presented can be used to c haracterize other classical rings such as pure-semisimple rings and perfec t rings.\n LOCATION:https://researchseminars.org/talk/OLS/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Reitzes (U of Chicago) DTSTART:20210415T180000Z DTEND:20210415T190000Z DTSTAMP:20260422T225801Z UID:OLS/42 DESCRIPTION:Title: Red uction games over $\\textup{RCA}_0$\nby Sarah Reitzes (U of Chicago) a s part of Online logic seminar\n\n\nAbstract\nIn this talk\, I will discus s joint work with Damir D. Dzhafarov and Denis R. Hirschfeldt. Our work ce nters on the characterization of problems P and Q such that P $\\leq_{\\om ega}$ Q\, as well as problems P and Q such that\n$\\textup{RCA}_0 \\vdash$ Q $\\to$ P\, in terms of winning strategies in certain games. These chara cterizations were originally introduced by Hirschfeldt and Jockusch. I wil l discuss extensions and generalizations of these characterizations\, incl uding a certain\nnotion of compactness that allows us\, for strategies sat isfying particular conditions\, to bound the number of moves it takes to w in. This bound is independent of the instance of the problem P being consi dered. This allows us to develop the idea of Weihrauch\nand generalized We ihrauch reduction over some base theory. Here\, we will focus on the base theory $\\textup{RCA}_0$. In this talk\, I will explore these notions of r eduction among various principles\, focusing particularly on bounding and induction principles.\n LOCATION:https://researchseminars.org/talk/OLS/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Ludovic Patey (Institut Camille Jordan\, Lyon) DTSTART:20210211T190000Z DTEND:20210211T200000Z DTSTAMP:20260422T225801Z UID:OLS/43 DESCRIPTION:Title: Can onical notions of forcing in computability theory\nby Ludovic Patey (I nstitut Camille Jordan\, Lyon) as part of Online logic seminar\n\n\nAbstra ct\nIn reverse mathematics\, a proof that a problem P does not imply a pro blem Q is usually done by constructing a computable instance of Q whose so lutions are computationally complex\, while proving that every simple inst ance of P has a simple solution\, using a notion of forcing. In its full g enerality\, the notion of forcing could depend on both P and Q\, but in mo st cases\, the notion of forcing for building solutions to P does not depe nd on Q. This suggests the existence of a "canonical" notion of forcing fo r P\, that is\, a notion of forcing such that all the relevant separation proofs can be obtained without loss of generality with sufficiently generi c sets for this notion. We settle a formal framework for discussing this q uestion\, and give preliminary results. This is a joint work with Denis Hi rschfeldt.\n LOCATION:https://researchseminars.org/talk/OLS/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Dakota Ihli (U of Illinois Urbana-Champaign) DTSTART:20210304T190000Z DTEND:20210304T200000Z DTSTAMP:20260422T225801Z UID:OLS/44 DESCRIPTION:Title: Wha t generic automorphisms of the random poset look like\nby Dakota Ihli (U of Illinois Urbana-Champaign) as part of Online logic seminar\n\n\nAbst ract\nThe random poset (the Fraïssé limit of the class of finite\nposets ) admits generic automorphisms — that is\, its automorphism group\nadmit s a comeagre conjugacy class. This result\, due to D. Kuske and J.\nTruss\ , was proven without explicitly describing the automorphisms in\nquestion. Here we give a new\, concrete description of the generic\nautomorphisms\, and we discuss the combinatorics and model theory involved.\n LOCATION:https://researchseminars.org/talk/OLS/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophia Knight (University of Minnesota\, Duluth) DTSTART:20210225T190000Z DTEND:20210225T200000Z DTSTAMP:20260422T225801Z UID:OLS/45 DESCRIPTION:Title: Rea soning about agents who may know other agents’ strategies in Strategy Lo gic\nby Sophia Knight (University of Minnesota\, Duluth) as part of On line logic seminar\n\n\nAbstract\nIn this talk I will discuss some new dev elopments in Strategy Logic with imperfect information. Strategy Logic is concerned with agents' strategic abilities in multi-agent systems\, and un like ATL\, treats strategies as first-class objects in the logic\, indepen dent from the agents. Thus\, in imperfect information settings\, Strategy Logic raises delicate issues\, such as what agents know about one another' s strategies. I will describe a new version of Strategy Logic that ensures that agents' strategies are uniform\, and allows a formal description of their knowledge about each other's strategies.\n LOCATION:https://researchseminars.org/talk/OLS/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Lieberman (Brno University of Technology) DTSTART:20210325T180000Z DTEND:20210325T190000Z DTSTAMP:20260422T225801Z UID:OLS/46 DESCRIPTION:Title: Rec ent developments in categorical model theory\nby Michael Lieberman (Br no University of Technology) as part of Online logic seminar\n\n\nAbstract \nWe give an overview of the foundations of the still-emerging field of ca tegorical model theory\, which synthesizes ideas and methods drawn from ac cessible categories\, abstract model theory\, and set theory. We discuss the fundamental nexus of interaction---a very slight generalization of abs tract elementary classes (AECs)---and sketch a few recent results. In par ticular\, we consider:\n-Connections between compact cardinals\, tameness of Galois types\, and the closure of images of accessible functors (joint work with Will Boney).\n-Stable independence on an abstract category\, wit h surprising connections to homotopy theory (joint work with Jiří Rosick ý and Sebastien Vasey).\n LOCATION:https://researchseminars.org/talk/OLS/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Moore (U of Kansas) DTSTART:20210311T190000Z DTEND:20210311T200000Z DTSTAMP:20260422T225801Z UID:OLS/47 DESCRIPTION:Title: The Hidden Subgroup Problem for Universal Algebras\nby Matthew Moore (U o f Kansas) as part of Online logic seminar\n\n\nAbstract\nThe Hidden Subgro up Problem (HSP) is a computational problem which includes as\nspecial cas es integer factorization\, the discrete logarithm problem\, graph\nisomorp hism\, and the shortest vector problem. The celebrated polynomial-time\nqu antum algorithms for factorization and the discrete logarithm are restrict ed\nversions of a generic polynomial-time quantum solution to the HSP for\ nabelian groups\, but despite focused research no polynomial-time s olution\nfor general groups has yet been found. We propose a generalizatio n of the HSP to\ninclude arbitrary algebraic structures and analyze this new problem on\npowers of 2-element algebras. We prove a complete cl assification of every such\npower as quantum tractable (i.e. polynomial-ti me)\, classically tractable\,\nquantum intractable\, or classically intrac table. In particular\, we identify a\nclass of algebras for which the gene ralized HSP exhibits super-polynomial\nspeedup on a quantum computer compa red to a classical one.\n LOCATION:https://researchseminars.org/talk/OLS/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Deirdre Haskell (McMaster University) DTSTART:20210401T180000Z DTEND:20210401T190000Z DTSTAMP:20260422T225801Z UID:OLS/48 DESCRIPTION:Title: Tam eness properties of theories of valued fields with analytic functions\ nby Deirdre Haskell (McMaster University) as part of Online logic seminar\ n\n\nAbstract\nAn important motif in model-theoretic algebra over the last thirty years has been the concept of tameness and the impact it has for u nderstanding the definable sets of a structure. In this talk\, I will desc ribe some of the ways this motif occurs in the case of valued fields\, esp ecially ordered convexly valued fields\, when equipped with additional fun ction symbols which\, on the standard model\, are interpreted by functions defined by convergent power series. All of these notions will be defined in the course of the talk.\n LOCATION:https://researchseminars.org/talk/OLS/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Mariana Vicaria (Berkeley) DTSTART:20210429T180000Z DTEND:20210429T190000Z DTSTAMP:20260422T225801Z UID:OLS/49 DESCRIPTION:Title: Eli mination of imaginaries and stable domination in multivalued fields\nb y Mariana Vicaria (Berkeley) as part of Online logic seminar\n\n\nAbstract \nThe model theory of henselian valued fields has been a major topic of st udy during the last century. Remarkable work has been achieved by Haskell\ , Hrushovski and Macpherson to understand the model theory of algebraicall y closed valued fields (ACVF). In a sequence of seminal papers they proved that this theory eliminates imaginaries once the geometric sorts are adde d and they developed the notion of stable domination\, which describes how types over maximally complete bases are controlled by the stable part of the structure. \n\n I will explain how to extend these results to the broader class of henselian valued fields of equicharacteristic zero\, res idue field algebraically closed and poly- regular value group. This includ es many interesting mathematical structures such as the Laurent Series ove r the Complex numbers\, but more importantly extends the results to valued fields with finitely many definable convex subgroups.\n LOCATION:https://researchseminars.org/talk/OLS/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentina Harizanov (George Washington University) DTSTART:20210506T180000Z DTEND:20210506T190000Z DTSTAMP:20260422T225801Z UID:OLS/50 DESCRIPTION:Title: Com putability theory and automorphisms of lattices of substructures\nby V alentina Harizanov (George Washington University) as part of Online logic seminar\n\n\nAbstract\nWe use computability-theoretic concepts and methods to study automorphisms of lattices of substructures of a canonical comput able infinite-dimensional vector space over the rationals. In particular\, we establish the equivalence of the embedding relation for certain automo rphism groups with the order relation of the corresponding Turing degrees. We further determine the Turing degrees of these automorphism groups. We establish similar results for the interval Boolean algebra over the ration als. This is joint work with Rumen Dimitrov and Andrei Morozov.\n LOCATION:https://researchseminars.org/talk/OLS/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Moorhead (University of Kansas) DTSTART:20210520T180000Z DTEND:20210520T190000Z DTSTAMP:20260422T225801Z UID:OLS/51 DESCRIPTION:Title: Hig her commutators\, hypercubes\, and the hierarchy of centralizer conditions \nby Andrew Moorhead (University of Kansas) as part of Online logic se minar\n\n\nAbstract\nThe commutator had historically been studied for spec ific varieties of algebras until Smith found a general definition for a co mmutator that worked for any Mal'cev algebra. Since then the commutator ha s become an essential part of the general algebraist's toolkit. Bulatov di scovered at the beginning of the century that the (binary) commutator can be extended to an infinite sequence of higher arity operations\, no one of which are term definable from the others. This discovery has most importa ntly led to the distinction between a nilpotent algebra and a 'supernilpot ent' algebra. While this distinction is invisible for groups\, supernilpot ent Mal'cev algebras share many strong properties with nilpotent groups\, while nilpotent algebras need not. We will discuss the extent to which som e of the known results of commutator theory can be viewed as a low-dimensi onal case of a general multidimensional theory.\n LOCATION:https://researchseminars.org/talk/OLS/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvy Anscombe (Université de Paris) DTSTART:20210422T180000Z DTEND:20210422T190000Z DTSTAMP:20260422T225801Z UID:OLS/52 DESCRIPTION:Title: Som e existential theories of fields\nby Sylvy Anscombe (Université de Pa ris) as part of Online logic seminar\n\n\nAbstract\nBuilding on previous w ork\, I will discuss Turing reductions between various fragments of theori es of fields. In particular\, we exhibit several theories of fields Turing equivalent to the existential theory of the rational numbers. This is joi nt work with Arno Fehm.\n LOCATION:https://researchseminars.org/talk/OLS/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrés Villaveces (Universidad Nacional de Colombia) DTSTART:20210513T180000Z DTEND:20210513T190000Z DTSTAMP:20260422T225801Z UID:OLS/53 DESCRIPTION:Title: A p artition relation for well-founded trees by Komjáth and Shelah\, and two applications to model theory.\nby Andrés Villaveces (Universidad Naci onal de Colombia) as part of Online logic seminar\n\n\nAbstract\nIn 2003\, Komjáth and Shelah proved a partition theorem on scattered order types\; these in turn could be understood as partition relations for classes of w ell-founded trees. Recently\, two different kinds of applications of the s ame partition relation have been used in infinitary logic and in model the ory: one by Väänänen and Velickovic on games related to Shelah’s logi c $L^1_\\kappa$\, another by Shelah and myself on the “canonical tree” of an AEC (a generalization of the Scott sentence for an abstract element ary class). I will describe the Komjáth-Shelah result in the first part a nd then narrow in the applications (with more details on the second one\, from some recent joint work with Shelah). Time permitting\, I will also ad dress a third interaction between partition relations and model theoretic issues.\n LOCATION:https://researchseminars.org/talk/OLS/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexi Block Gorman (University of Illinois Urbana-Champaign) DTSTART:20210527T180000Z DTEND:20210527T190000Z DTSTAMP:20260422T225801Z UID:OLS/54 DESCRIPTION:Title: Def inability on the Reals from Büchi Automata\nby Alexi Block Gorman (Un iversity of Illinois Urbana-Champaign) as part of Online logic seminar\n\n \nAbstract\nBüchi automata are the natural analogue of finite automata in the context of infinite strings (indexed by the natural numbers) on a fin ite alphabet. We say a subset X of the reals is r-regular if there is a B üchi automaton that accepts (one of) the base-r representations of every element in X\, and rejects the base-r representations of each element in i ts complement. These sets often exhibit fractal-like behavior—e.g.\, the Cantor set is 3-regular. There are remarkable connections in logic to Bü chi automata\, particularly in model theory. In this talk\, I will give a characterization of when the expansion of the real ordered additive group by a predicate for a closed r-regular subset of [0\,1] is model-theoretica lly tame (d-minimal\, NIP\, NTP2). Moreover\, I will discuss how this coi ncides with geometric tameness\, namely trivial fractal dimension. This w ill include a discussion of how the properties of definable sets vary depe nding on the properties of the Büchi automaton that recognizes the predic ate subset.\n LOCATION:https://researchseminars.org/talk/OLS/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Dimitra Chompitaki (University of Crete) DTSTART:20210708T180000Z DTEND:20210708T190000Z DTSTAMP:20260422T225801Z UID:OLS/55 DESCRIPTION:Title: Dec idability results of subtheories of commonly used domains in Algebra and N umber Theory\nby Dimitra Chompitaki (University of Crete) as part of O nline logic seminar\n\n\nAbstract\nWe will present some known decidability and undecidability results for theories of the ring-structures of commonl y used domains (Polynomial Rings\, Rational Functions\, Formal Power Serie s). Then we will focus on ongoing research relating to some subtheories su ch as: (a) Addition and the Frobenius map for subrings of Rational Functio ns of positive characteristic\, and (b) Addition and Divisibility for Form al Power Series. The latter results fall mostly on the "decidability" side : model completeness and elimination of quantifiers.\n LOCATION:https://researchseminars.org/talk/OLS/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Christina Brech (Universidade de São Paulo) DTSTART:20210617T180000Z DTEND:20210617T190000Z DTSTAMP:20260422T225801Z UID:OLS/56 DESCRIPTION:Title: Iso morphic combinatorial families\nby Christina Brech (Universidade de S ão Paulo) as part of Online logic seminar\n\n\nAbstract\nWe will recall t he notion of compact and hereditary families of finite subsets of some car dinal κ and their corresponding combinatorial Banach spaces. We present a combinatorial version of Banach-Stone theorem\, which leads naturally to a notion of isomorphism between families. Our main result shows that diffe rent families on ω are not isomorphic\, if we assume them to be spreading . We also discuss the difference between the countable and the uncountable setting. This is a joint work with Claribet Piña.\n LOCATION:https://researchseminars.org/talk/OLS/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo Arena (Pontificia Universidad Católica de Chile) DTSTART:20210909T180000Z DTEND:20210909T190000Z DTSTAMP:20260422T225801Z UID:OLS/57 DESCRIPTION:Title: Des criptive Complexity for Counting Complexity Classes\nby Marcelo Arena (Pontificia Universidad Católica de Chile) as part of Online logic semina r\n\n\nAbstract\nDescriptive Complexity has been very successful in charac terizing complexity classes of decision problems in terms of the propertie s definable in some logics. However\, descriptive complexity for counting complexity classes\, such as FP and #P\, has not been systematically studi ed\, and it is not as developed as its decision counterpart. In this talk\ , we will present a framework based on Weighted Logics to address this iss ue. Specifically\, by focusing on the natural numbers we obtain a logic ca lled Quantitative Second Order Logics (QSO)\, and show how some of its fra gments can be used to capture fundamental counting complexity classes such as FP\, #P and FPSPACE\, among others. Moreover\, we use QSO to define a hierarchy inside #P\, identifying counting complexity classes with good cl osure and approximation properties\, and which admit natural complete prob lems.\n LOCATION:https://researchseminars.org/talk/OLS/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Nagloo (University of Illinois Chicago) DTSTART:20210819T180000Z DTEND:20210819T190000Z DTSTAMP:20260422T225801Z UID:OLS/58 DESCRIPTION:Title: Geo metric triviality in differentially closed fields\nby Joel Nagloo (Uni versity of Illinois Chicago) as part of Online logic seminar\n\n\nAbstract \nIn this talk we revisit the problem of describing the 'finer' structure of geometrically trivial strongly minimal sets in $DCF_0$. In particular\, I will explain how recent work joint with Guy Casale and James Freitag on Fuchsian groups (discrete subgroup of $SL_2(\\mathbb{R})$) and automorphi c functions\, has lead to intriguing questions around the $\\omega$-catego ricity conjecture of Daniel Lascar. This conjecture was disproved in its f ull generality by James Freitag and Tom Scanlon using the modular group $S L_2(\\mathbb{Z})$ and its automorphic uniformizer (the $j$-function). I wi ll explain how their counter-example fits into the larger context of arith metic Fuchsian groups and has allowed us to 'propose' refinements to the o riginal conjecture.\n LOCATION:https://researchseminars.org/talk/OLS/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachael Alvir (University of Notre Dame) DTSTART:20210610T180000Z DTEND:20210610T190000Z DTSTAMP:20260422T225801Z UID:OLS/60 DESCRIPTION:Title: Sco tt Complexity and Finitely α-generated Structures\nby Rachael Alvir ( University of Notre Dame) as part of Online logic seminar\n\n\nAbstract\nI n this talk\, we define the notion of a finitely α-generated structure an d generalize results about Scott sentences earlier known only for finitely generated structures. We will show how these results can be used to the c onnect some of the existing non-equivalent definitions of Scott rank.\n LOCATION:https://researchseminars.org/talk/OLS/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Tarek Sayed-Ahmed (Cairo University) DTSTART:20210603T180000Z DTEND:20210603T190000Z DTSTAMP:20260422T225801Z UID:OLS/61 DESCRIPTION:Title: Ato m canonicity\, complete representations\, and omitting types\nby Tarek Sayed-Ahmed (Cairo University) as part of Online logic seminar\n\n\nAbstr act\nClick here for abstract\n LOCATION:https://researchseminars.org/talk/OLS/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Daoud Siniora (American University in Cairo) DTSTART:20210701T180000Z DTEND:20210701T190000Z DTSTAMP:20260422T225801Z UID:OLS/62 DESCRIPTION:Title: Gen eric automorphisms of homogeneous structures\nby Daoud Siniora (Americ an University in Cairo) as part of Online logic seminar\n\n\nAbstract\nAut omorphism groups of countable first-order structures are Polish groups und er the pointwise convergence topology. An automorphism is called generic i f its conjugacy class in comeagre. In this talk we focus on generic automo rphisms of homogeneous structures\, such structures arise as Fraisse limit s of amalgamation classes of finite structures. We will present joint work with Itay Kaplan and Tomasz Rzepecki studying generic automorphisms of th e countable universal homogeneous meet-tree.\n LOCATION:https://researchseminars.org/talk/OLS/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristobal Rojas (Pontificia Universidad Católica de Chile) DTSTART:20210715T180000Z DTEND:20210715T190000Z DTSTAMP:20260422T225801Z UID:OLS/63 DESCRIPTION:Title: Com putability of Harmonic Measure\nby Cristobal Rojas (Pontificia Univers idad Católica de Chile) as part of Online logic seminar\n\n\nAbstract\nAb stract: We will review recent results relating the geometry of a connecte d domain to the computability of its harmonic measure at a given point x. In particular\, we will discuss examples of domains whose harmonic measure at x is always computable relative to x\, but not uniformly. This constru ction gives rise to examples of continuous functions arising as solutions to a Dirichlet problem (so they are even harmonic) which are piecewise com putable (i.e. all their values are computable relative to the input point) \, but not computable.\n LOCATION:https://researchseminars.org/talk/OLS/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristina Sernadas (Universidade de Lisbona) DTSTART:20210902T180000Z DTEND:20210902T190000Z DTSTAMP:20260422T225801Z UID:OLS/64 DESCRIPTION:Title: Dec idability via Reduction in Logics and Their Combinations\nby Cristina Sernadas (Universidade de Lisbona) as part of Online logic seminar\n\n\nAb stract\nDecision problems in logic include semantic based problems like th e satisfiability and the validity problems\nand deductive problems like th e theoremhood and the consequence problems. Satisfaction systems and reduc tions between \nthem are presented as an appropriate context for analyzing the satisfiability and the validity problems. \nThe notion of reduction is generalized in order to cope with the meet-combination of logics.\nRed uctions between satisfaction systems induce reductions between the respect ive satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisf iability problems to validity problems. Reflection results for decidabilit y in the presence of reductions are established. The validity problem in t he meet-combination is proved to be decidable\nwhenever the validity prob lems for the components are decidable. Some examples are discussed\, name ly\, the meet-combination of modal logic and intuitionistic logic. Some o ngoing work related to consequence problems in the context of consequence systems and their combination is pointed out. \nThis talk reports on joint work with João Rasga and Walter Carnielli.\n LOCATION:https://researchseminars.org/talk/OLS/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford) DTSTART:20210729T180000Z DTEND:20210729T190000Z DTSTAMP:20260422T225801Z UID:OLS/65 DESCRIPTION:Title: Pro babilistic Littlewood-Offord anti-concentration results via model theory\nby Hunter Spink (Stanford) as part of Online logic seminar\n\n\nAbstra ct\nAbstract: (Joint with Jacob Fox and Matthew Kwan) The classical Erdos- Littlewood-Offord theorem says that for any n nonzero vectors in $R^d$\, a random signed sum concentrates on any point with probability at most $O(n ^{-1/2})$. Combining tools from probability theory\, additive combinatoric s\, and model theory\, we obtain an anti-concentration probability of $n^{ -1/2+o(1)}$ for any o-minimal set $S$ in $R^d$ (such as a hypersurface def ined by a polynomial in $x_1\,...\,x_n\,e^{x_1}\,...\,e^{x_n}$\, or a rest ricted analytic function) not containing a line segment. We do this by sho wing such o-minimal sets have no higher-order additive structure\, complem enting work by Pila on lower-order additive structure developed to count r ational and algebraic points of bounded height.\n LOCATION:https://researchseminars.org/talk/OLS/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Colin Jahel (Université Claude Bernard Lyon 1) DTSTART:20210826T180000Z DTEND:20210826T190000Z DTSTAMP:20260422T225801Z UID:OLS/66 DESCRIPTION:Title: Som e progress on the unique ergodicity problem\nby Colin Jahel (Universit é Claude Bernard Lyon 1) as part of Online logic seminar\n\n\nAbstract\nI n 2005\, Kechris\, Pestov and Todorcevic exhibited a\ncorrespondence betwe en combinatorial properties of structures and\ndynamical properties of the ir automorphism groups. In 2012\, Angel\,\nKechris and Lyons used this cor respondence to show the unique ergodicity\nof all the minimal actions of s ome subgroups of $S_\\infty$. In this\ntalk\, I will give an overview of t he aforementioned results and discuss\nrecent work generalizing results of Angel\, Kechris and Lyons in several\ndirections.\n LOCATION:https://researchseminars.org/talk/OLS/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Schweber (Proof School) DTSTART:20210722T180000Z DTEND:20210722T190000Z DTSTAMP:20260422T225801Z UID:OLS/67 DESCRIPTION:Title: Cee rs higher up\nby Noah Schweber (Proof School) as part of Online logic seminar\n\n\nAbstract\nAbstract: We examine analogues of ceers (computably enumerable equivalence relations) in generalized recursion theory - speci fically\, in $\\kappa$-recursion theory for $\\kappa$ an uncountable regul ar cardinal. Classically\, the degrees of ceers with respect to computable embeddability forms a partial order which is maximally complicated\, name ly one whose theory is computably isomorphic to that of true arithmetic. W e extend this result to the $\\kappa$-ceers. Interestingly\, this requires a genuinely new argument\, and currently no single approach is known whic h applies both to $\\omega$ and to uncountable regular $\\kappa$. Moreover \, the situation for singular cardinals\, let alone admissible ordinals wh ich are not cardinals such as $\\omega_1^{CK}$\, is completely open. If ti me permits\, we will discuss a second proof of the above result for the sp ecial case of $\\kappa=\\omega_1$ which has the advantage of applying to c ertain generalized computability theories other than $\\kappa$-recursion t heories.\n\nThis is joint work with Uri Andrews\, Steffen Lempp\, and Mana t Mustafa.\n LOCATION:https://researchseminars.org/talk/OLS/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Gregory Cherlin (Rutgers University) DTSTART:20211021T180000Z DTEND:20211021T190000Z DTSTAMP:20260422T225801Z UID:OLS/68 DESCRIPTION:Title: Hom ogeneity and generalized metric spaces\nby Gregory Cherlin (Rutgers Un iversity) as part of Online logic seminar\n\n\nAbstract\nGeneralized metri c spaces of various sorts have come up in\nconnection with the study of ho mogeneous structures (classification\,\nRamsey theoretic properties). I'll discuss examples studied by Sauer\,\nConant\, Braunfeld\, Hubi&ccaron\;ka \, Kone&ccaron\;ný\;\, Ne&scaron\;et&rcaron\;il\, and others. See\, notably\, Kone&ccaron\;ný\;'s master's thesis (arXiv).\n LOCATION:https://researchseminars.org/talk/OLS/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Shlapentokh (East Carolina University) DTSTART:20211028T180000Z DTEND:20211028T190000Z DTSTAMP:20260422T225801Z UID:OLS/69 DESCRIPTION:Title: A M ysterious Ring\nby Alexandra Shlapentokh (East Carolina University) as part of Online logic seminar\n\n\nAbstract\nLet ${\\mathbb Q}^{\\text{ab} }$ be the largest abelian extension of $\\mathbb Q$\, or in other words th e compositum of all cyclotomic extensions. Let $O_{{\\mathbb Q}^{\\text{a b}}}$ be the ring of integers of ${\\mathbb Q}^{\\text{ab}}$ or the ring o f elements of ${\\mathbb Q}^{\\text{ab}}$ satisfying monic irreducible pol ynomials over $\\mathbb Z$. It is not known whether the first-order theor y of $O_{{\\mathbb Q}^{\\text{ab}}}$ is decidable. ${\\mathbb Q}^{\\text{ ab}}$ is also a degree two extension of a totally real field. Much more i s known about the first-order theory of rings of integers of totally real fields and in some cases one is able to deduce undecidability of the first -order theory of the ring of integers of a degree 2 extension of a totall y real field from an analogous result for the ring of integers of the tota lly real field. However this method does not seem to work for ${\\mathbb Q}^{\\text{ab}}$. We discuss a possible way of resolving this problem and some related questions.\n LOCATION:https://researchseminars.org/talk/OLS/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Caroline Terry (Ohio State University) DTSTART:20210916T180000Z DTEND:20210916T190000Z DTSTAMP:20260422T225801Z UID:OLS/70 DESCRIPTION:Title: Spe eds of hereditary properties and mutual algebricity\nby Caroline Terry (Ohio State University) as part of Online logic seminar\n\n\nAbstract\nA hereditary graph property is a class of finite graphs closed under isomorp hism and induced subgraphs. Given a hereditary graph property H\, the spe ed of H is the function which sends an integer n to the number of distinct elements in H with underlying set {1\,...\,n}. Not just any function can occur as the speed of hereditary graph property. Specifically\, there ar e discrete ``jumps" in the possible speeds. Study of these jumps began wi th work of Scheinerman and Zito in the 90's\, and culminated in a series o f papers from the 2000's by Balogh\, Bollob\\'{a}s\, and Weinreich\, in wh ich essentially all possible speeds of a hereditary graph property were ch aracterized. In contrast to this\, many aspects of this problem in the hy pergraph setting remained unknown. In this talk we present new hypergraph analogues of many of the jumps from the graph setting\, specifically thos e involving the polynomial\, exponential\, and factorial speeds. The jump s in the factorial range turned out to have surprising connections to the model theoretic notion of mutual algebricity\, which we also discuss. Thi s is joint work with Chris Laskowski.\n LOCATION:https://researchseminars.org/talk/OLS/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Franziska Jahnke (University of Münster) DTSTART:20211014T180000Z DTEND:20211014T190000Z DTSTAMP:20260422T225801Z UID:OLS/71 DESCRIPTION:Title: Dec idability and definability in unramified henselian valued fields\nby F ranziska Jahnke (University of Münster) as part of Online logic seminar\n \n\nAbstract\nUnramified and finitely ramified henselian valued fields are \ncentral to studying model-theoretic phenomena in mixed characteristic.\n Decidability and definability in unramified henselian valued fields with\n perfect residue field are well understood\, starting with the seminal\nwor k of Ax\, Kochen\, and Ershov. In this talk\, we present recent\ndevelopme nts in unramified henselian valued fields with imperfect\nresidue field\, and also comment on what changes in the case of finite\nramification. This is joint work with Sylvy Anscombe.\n LOCATION:https://researchseminars.org/talk/OLS/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Uckelman (Durham University) DTSTART:20211118T190000Z DTEND:20211118T200000Z DTSTAMP:20260422T225801Z UID:OLS/72 DESCRIPTION:Title: Joh n Eliot's Logick Primer: A bilingual English-Algonquian logic textb ook\nby Sara Uckelman (Durham University) as part of Online logic semi nar\n\n\nAbstract\nIn 1672 John Eliot\, English Puritan educator and missi onary\, published The Logick Primer: Some Logical Notions to initiate t he INDIANS in the knowledge of the Rule of Reason\; and to know how to mak e use thereof [1]. This roughly 80 page pamphlet focuses on introduci ng basic syllogistic vocabulary and reasoning so that syllogisms can be cr eated from texts in the Psalms\, the gospels\, and other New Testament boo ks. The use of logic for proselytizing purposes is not distinctive: What is distinctive about Eliot's book is that it is bilingual\, written in bot h English and Massachusett\, an Algonquian language spoken in eastern coas tal and southeastern Massachusetts. It is one of the earliest bilingual l ogic textbooks\, it is the only textbook that I know of in an indigenous A merican language\, and it is one of the earliest printed attestations of t he Massachusett language.\n\n

In this talk\, I will:\n

\n\n[1] J.[ohn] E.[liot]. The Logick Primer: Some Logical Notions to initiate the INDI ANS in the knowledge of the Rule of Reason\; and to know how to make use t hereof. Printed by M. J.\, 1672\n LOCATION:https://researchseminars.org/talk/OLS/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Jana Mařiková (Universität Wien) DTSTART:20211111T190000Z DTEND:20211111T200000Z DTSTAMP:20260422T225801Z UID:OLS/73 DESCRIPTION:Title: Def inable matchings in o-minimal bipartite graphs\nby Jana Mařiková (Un iversität Wien) as part of Online logic seminar\n\n\nAbstract\nThis talk will revolve around the question\, under what conditions an o-minimally de finable bipartite graph admits a\ndefinable matching. We discuss some con text\, a partial result\, and touch on possible applications. This\nis wo rk in progress.\n LOCATION:https://researchseminars.org/talk/OLS/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Natalia García Fritz (Pontificia Universidad Católica de Chile) DTSTART:20211104T180000Z DTEND:20211104T190000Z DTSTAMP:20260422T225801Z UID:OLS/74 DESCRIPTION:Title: Hil bert's tenth problem for rings of exponential polynomials\nby Natalia García Fritz (Pontificia Universidad Católica de Chile) as part of Onlin e logic seminar\n\n\nAbstract\nAfter being negatively solved by Davis\, Pu tnam\, Robinson\, and Matijasevich in 1970\, Hilbert’s tenth problem has been extended to a number of other rings. One of the main natural open ca ses is that of the ring of complex entire functions in one variable. After reviewing some literature around this problem\, in this talk I will outli ne a negative solution of the analogue of Hilbert's tenth problem for the ring of exponential polynomials\, approaching the case of entire functions . This is joint work with D. Chompitaki\, H. Pasten\, T. Pheidas\, and X. Vidaux.\n LOCATION:https://researchseminars.org/talk/OLS/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Françoise Point (Université de Mons-Hainaut) DTSTART:20211007T180000Z DTEND:20211007T190000Z DTSTAMP:20260422T225801Z UID:OLS/75 DESCRIPTION:Title: Def inable groups in topological fields with a generic derivation\nby Fran çoise Point (Université de Mons-Hainaut) as part of Online logic seminar \n\n\nAbstract\nWe study a class of tame $\\mathcal L$-theories $T$ of top ological fields and their extensions by a generic derivation $\\delta$. Th e topological fields under consideration include henselian valued fields o f characteristic 0 and real closed fields. We axiomatize the class of the existentially closed $\\mathcal L_\\delta$-expansions.\nWe show that $T_\\ delta^*$ has $\\mathcal L$-open core (i.e.\, every $\\mathcal L_\\delta$-d efinable open set is $\\mathcal L$-definable) and derive both a cell decom position theorem and a transfer result of elimination of imaginaries. Othe r tame properties of $T$ such as relative elimination of field sort quanti fiers\, NIP and distality also transfer to $T_\\delta^*$. \n\\par Then let ting $\\mathcal K$ be a model of $T_\\delta^*$ and $\\mathcal M$ a $\\vert K\\vert^+$-saturated elementary extension of $\\mathcal K$\, we first ass ociate with an $\\mathcal L_\\delta(K)$-definable group $G$ in $\\mathcal M$\, a pro-$\\mathcal L$-definable set $G^{**}_{\\infty}$ in which the dif ferential prolongations $G^{\\nabla_\\infty}$ of elements of $G$ are dense \, using the $\\mathcal L$-open core property of $T_\\delta^*$. Following the same ideas as in the group configuration theorem in o-minimal structur es as developed by K. Peterzil\, we construct a type $\\mathcal L$-definab le topological group $H_\\infty\\subset G^{**}_{\\infty}$\, acting on a $K $-infinitesimal neighbourhood of a generic element of $G^{**}_\\infty$ in a faithful\, continuous and transitive way. Further $H_\\infty\\cap G^{\\n abla_\\infty}$ is dense in $H_\\infty$ and the action of $H_\\infty\\cap G ^{\\nabla_\\infty}$ coincides with the one induced by the initial $\\mathc al L_\\delta$-group action. \n\\par The first part of this work is joint w ith Pablo Cubid\\`es Kovacsics.\n LOCATION:https://researchseminars.org/talk/OLS/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Vasco Brattka (Universität der Bundeswehr München) DTSTART:20211202T190000Z DTEND:20211202T200000Z DTSTAMP:20260422T225801Z UID:OLS/77 DESCRIPTION:Title: A G alois connection between Turing jumps and limits\nby Vasco Brattka (Un iversität der Bundeswehr München) as part of Online logic seminar\n\n\nA bstract\nWe discuss a Galois connection between Turing jumps and limits\nt hat offers a fresh view on the class of limit computable functions\nand it s properties. This view does not only offer simplified proofs\nof many kno wn classical results in computable analysis\, but also\nnew insights. With this approach we also propagate a more uniform\nview on computability the ory in general.\n LOCATION:https://researchseminars.org/talk/OLS/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Gihanee Senadheera (Southern Illinois University) DTSTART:20210930T180000Z DTEND:20210930T190000Z DTSTAMP:20260422T225801Z UID:OLS/78 DESCRIPTION:Title: Eff ective Concept Classes of PACi/PAC Incomparable Degrees and Jump Structure \nby Gihanee Senadheera (Southern Illinois University) as part of Onli ne logic seminar\n\n\nAbstract\nThe Probably Approximately Correct (PAC) l earning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size a nd computation time. This reducibility in PAC learning resembles the reduc ibility in Turing computability. In 1957 Friedberg and Muchnik independent ly solved the Post problem by constructing computably enumerable sets $A$ and $B$ of incomparable degrees using the priority construction method. We adapt this idea to PACi/PAC reducibilities and construct two the effectiv e concept classes $C_0$ and $C_1$ such that $C_0$ is not reducible to $C_1 $ and vice versa. When considering PAC reducibility it was necessary to wo rk on the size of an effective concept class\, thus we use Kolmogorov comp lexity to obtain the size. Analogous to Turing jump\, we give a jump struc ture on effective concept classes. As the future work\, we begin to explor e an embedding of structures from PAC degrees to 1-1 degrees or Turing deg rees.\n LOCATION:https://researchseminars.org/talk/OLS/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Mostafa Mirabi (Wesleyan University) DTSTART:20211209T190000Z DTEND:20211209T200000Z DTSTAMP:20260422T225801Z UID:OLS/79 DESCRIPTION:Title: MS- measurability via Coordinatization\nby Mostafa Mirabi (Wesleyan Univer sity) as part of Online logic seminar\n\n\nAbstract\nAbstract: In this tal k\, we first discuss the concept of MS-measurable structures\, introduced by Macpherson and Steinhorn in 2007. Then we will define a strong notion o f Coordinatization for $\\aleph_0$-categorical structures and show that a structure which is coordinatized by $\\aleph_0$-categorical MS-measurable structures itself is MS-measurable. This approach provides a way to build new MS-measurable structures.\n LOCATION:https://researchseminars.org/talk/OLS/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Todor Tsankov (Institut Camille Jordan) DTSTART:20211216T190000Z DTEND:20211216T200000Z DTSTAMP:20260422T225801Z UID:OLS/80 DESCRIPTION:Title: Con tinuous logic and Borel equivalence relations\nby Todor Tsankov (Insti tut Camille Jordan) as part of Online logic seminar\n\n\nAbstract\nThe the ory of Borel reducibility of definable equivalence relations\nwas initiate d by Friedman and Stanley who were specifically interested\nin the equival ence relation of isomorphism of countable structures.\nSince then\, the sc ope of the theory has considerably expanded but\nisomorphism of countable structures remains one of the situations\nwhere the most detailed results are available and where both methods of\ninfinitary model theory and descr iptive set theory can be applied. In\nthis talk\, I will explain how infin itary continuous logic can be used\nto extend parts of this theory to metr ic structures. Our main result\nis about isomorphism of locally compact me tric structures and it is\na common generalization of theorems of Hjorth ( for locally compact\nmetric spaces) and Hjorth and Kechris (for countable structures). This\nis joint work with Andreas Hallbä\;ck and Maciej Ma licki.\n LOCATION:https://researchseminars.org/talk/OLS/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Lauren Wickman (University of Florida) DTSTART:20220127T190000Z DTEND:20220127T200000Z DTSTAMP:20260422T225801Z UID:OLS/81 DESCRIPTION:Title: Kna ster Continua and Projective Fraïssé Theory\nby Lauren Wickman (Univ ersity of Florida) as part of Online logic seminar\n\n\nAbstract\nThe Knas ter continuum\, also known as the buckethandle\, or the Brouwer–Janiszew ski–Knaster continuum can be viewed as an inverse limit of 2-tent maps o n the interval. However\, there is a whole class (with continuum many non- homeomorphic members) of Knaster continua\, each viewed as an inverse limi t of p-tent maps\, where p is a sequence of primes. In this talk\, for eac h Knaster continuum K\, we will give a projective Fraïssé class of finit e objects that approximate K (up to homeomorphism) and examine the combina torial properties of that the class (namely whether the class is Ramsey or if it has a Ramsey extension). We will give an extremely amenable subgrou p of the homeomorphism group of the universal Knaster continuum.\n LOCATION:https://researchseminars.org/talk/OLS/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Caleb Camrud (Iowa State University) DTSTART:20220113T190000Z DTEND:20220113T200000Z DTSTAMP:20260422T225801Z UID:OLS/82 DESCRIPTION:Title: Con tinuous Logic\, Diagrams\, and Truth Values for Computable Presentations\nby Caleb Camrud (Iowa State University) as part of Online logic semina r\n\n\nAbstract\nGoldbring\,McNicholl\, and I investigated the arithmetic and hyperarithmetic degrees of the finitary and computable infinitary diag rams of continuous logic for computably presented metric structures. As th e truth value of a sentence of continuous logic may be any real in [0\,1]\ , we introduced two kinds of diagrams at each level: the closed diagram\, which encapsulates weak inequalities of truth values\, and the open diagra m\, which encapsulates strict inequalities. We showed that\, for any compu tably presented metric structure and any computable ordinal $\\alpha$\, th e closed and open $\\Sigma^c_\\alpha$ diagrams are $\\Pi^0_{\\alpha+1}$ an d $\\Sigma^0_\\alpha$\, respectively\, and that the closed and open $\\Pi^ c_\\alpha$ diagrams are $\\Pi^0_\\alpha$ and $\\Sigma^0_{\\alpha+1}$.\n\nP roving the optimality of these bounds\, however\, was non-trivial. Since t he standard presentation of [0\,1] with the Euclidean metric is computably compact\, we were forced to work on the natural numbers with the discrete metric (in some sense\, the "simplest" non-compact metric space). Along t he way\, we also proved some surprising combinatorial results. McNicholl a nd I then continued our study of computable infinitary continuous logic an d found that for any nonzero computable ordinal $\\alpha$ and any right $\ \Pi^0_\\alpha$ (or $\\Sigma^0_\\alpha$) real number\, there is a $\\Pi^c_\ \alpha$ (or $\\Sigma^c_\\alpha$) sentence which is universally interpreted as that value.\n LOCATION:https://researchseminars.org/talk/OLS/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Turetsky (Victoria University of Wellington) DTSTART:20220120T190000Z DTEND:20220120T200000Z DTSTAMP:20260422T225801Z UID:OLS/83 DESCRIPTION:Title: Tru e Stages -- From Priority Arguments to Descriptive Set Theory\nby Dani el Turetsky (Victoria University of Wellington) as part of Online logic se minar\n\n\nAbstract\nThe true stages machinery was conceived as a techniqu e for organizing complex priority constructions in computability theory\, much like Ash's metatheorem. With a little modification\, however\, it ca n prove remarkably useful in descriptive set theory. Using this machinery \, we can obtain nice proofs of results of Wadge\, Hausdorff and Kuratowsk i\, and Louveau\, sometimes strengthening the result in the process.\nWith out getting too deep into the details\, I will give the ideas of the machi nery and how it applies to descriptive set theory.\n LOCATION:https://researchseminars.org/talk/OLS/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Roman Kossak (Graduate Center\, City University of New York) DTSTART:20220224T190000Z DTEND:20220224T200000Z DTSTAMP:20260422T225801Z UID:OLS/84 DESCRIPTION:Title: Und efinability and absolute undefinability in models of arithmetic\nby Ro man Kossak (Graduate Center\, City University of New York) as part of Onli ne logic seminar\n\n\nAbstract\nI will survey some well-known and some mor e recent undefinability results about models of Peano Arithmetic. I want t o contrast first-order undefinability in the standard model with a much st ronger notion of undefinability which is suitable for resplendent models\ , and use the results to motivate some more general questions about the na ture of undefinability.\n LOCATION:https://researchseminars.org/talk/OLS/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Adam Case (Drake University) DTSTART:20220303T190000Z DTEND:20220303T200000Z DTSTAMP:20260422T225801Z UID:OLS/85 DESCRIPTION:Title: Fin ite-State Mutual Dimension\nby Adam Case (Drake University) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, I will discuss recent work with Jack H. Lutz on a notion of finite-state mutual dimension. Intui tively\, the finite-state dimension of a sequence S represents the density of finite-state information contained within S\, while the finite-state m utual dimension between two sequences S and T represents the density of fi nite-state information shared by S and T. Thus "finite-state mutual dimens ion" can be viewed as a "finite-state" version of mutual dimension and as a "mutual" version of finite-state dimension. The main results that will b e discussed are as follows. First\, we show that finite-state mutual dimen sion\, defined using information-lossless finite-state compressors\, has a ll of the properties expected of a measure of mutual information. Next\, w e prove that finite-state mutual dimension may be characterized in terms o f block mutual information rates. Finally\, we provide necessary and suffi cient conditions for two normal sequences to achieve finite-state mutual d imension zero.\n LOCATION:https://researchseminars.org/talk/OLS/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonina Kolokolova (Memorial University of Newfoundland) DTSTART:20220210T190000Z DTEND:20220210T200000Z DTSTAMP:20260422T225801Z UID:OLS/86 DESCRIPTION:Title: Lea rning from bounded arithmetic\nby Antonina Kolokolova (Memorial Univer sity of Newfoundland) as part of Online logic seminar\n\n\nAbstract\nThe c entral question of complexity theory -- what can (and cannot) be feasibly computed -- has a corresponding logical meta-question: what can (and cann ot) be feasibly proven. While complexity theory studies the former\, boun ded arithmetic is one of the main approaches to the meta-question. There i s a tight relation between theories of bounded arithmetic and correspondin g complexity classes\, allowing one to study what can be proven in\, for e xample\, "polynomial-time reasoning" and what power is needed to resolve c omplexity questions\, with a number of both positive and negative provabil ity results.\n\nHere\, we focus on the complexity of another meta-problem: learning to solve problems such as Boolean satisfiability. There is a ran ge of ways to define "solving problems"\, with one extreme\, the uniform s etting\, being an existence of a fast algorithm (potentially randomized)\ , and another of a potentially non-computable family of small Boolean circ uits\, one for each problem size. The complexity of learning can be recas t as the complexity of finding a procedure to generate Boolean circuits so lving the problem of a given size\, if it (and such a family of circuits) exists.\n\nFirst\, inspired by the KPT witnessing theorem\, a special cas e of Herbrand's theorem in bounded arithmetic\, we develop an intermediate notion of uniformity that we call LEARN-uniformity. While non-uniform lo wer bounds are notoriously difficult\, we can prove several unconditional lower bounds for this weaker notion of uniformity. Then\, returning to th e world of bounded arithmetic and using that notion of uniformity as a too l\, we show unprovability of several complexity upper bounds for both dete rministic and randomized complexity classes\, in particular giving simpler proofs that the theory of polynomial-time reasoning PV does not prove tha t all of P is computable by circuits of a specific polynomial size\, and t he theory $V^1$\, a second-order counterpart to the classic Buss' theory $ S^1_2$\, does not prove the same statement with NP instead of P. \n\nFina lly\, we leverage these ideas to show that bounded arithmetic "has trouble differentiating" between uniform and non-uniform frameworks: more specif ically\, we show that theories for polynomial-time and randomized polynom ial-time reasoning cannot prove both a uniform lower bound and a non-unif orm upper bound for NP. In particular\, while it is possible that NP != P yet all of NP is computable by families of polynomial-size circuits\, th is cannot be proven feasibly.\n LOCATION:https://researchseminars.org/talk/OLS/86/ END:VEVENT BEGIN:VEVENT SUMMARY:John Baldwin (University of Illinois\, Chicago) DTSTART:20220317T180000Z DTEND:20220317T190000Z DTSTAMP:20260422T225801Z UID:OLS/87 DESCRIPTION:Title: Cat egory theory and Model Theory: Symbiotic Scaffolds\nby John Baldwin (U niversity of Illinois\, Chicago) as part of Online logic seminar\n\n\nAbst ract\nA scaffold for mathematics includes both local foundat ions for\nvarious areas of mathematics and productive guidance in how to u nify them. In\na scaffold the unification does not take place by a common axiomatic basis\nbut consists of a systematic ways of connecting results a nd proofs in various\nareas of mathematics. Two scaffolds\, model theory and category theory\,\nprovide local foundations for many areas of mathema tic including two flavors\n(material and structural) of set theory and di fferent approaches to\nunification. We will discuss salient features of th e two scaffolds including\ntheir contrasting but bi-interpretable set theo ries. We focus on the\ncontrasting treatments of `size' in each scaffold a nd the\n advantages/disadvantages of each for different problems.\n LOCATION:https://researchseminars.org/talk/OLS/87/ END:VEVENT BEGIN:VEVENT SUMMARY:George Metcalfe (University of Bern) DTSTART:20220428T180000Z DTEND:20220428T190000Z DTSTAMP:20260422T225801Z UID:OLS/88 DESCRIPTION:Title: Fro m ordered groups to ordered monoids and back again\nby George Metcalfe (University of Bern) as part of Online logic seminar\n\n\nAbstract\n(Join t work with Almudena Colacito\, Nikolaos Galatos\, and Simon Santschi)\n\n Removing the inverse operation from any lattice-ordered group (l-group)\, such as the ordered additive group of integers\, produces a distributive l attice-ordered monoid (l-monoid)\, but it is not the case that every distr ibutive l-monoid admits a group structure. In particular\, every l-group e mbeds into an l-group of automorphisms of some chain and is either trivial or infinite\, whereas every distributive l-monoid embeds into a possibly finite l-monoid of endomorphisms of some chain.\n\nIn this talk\, we will see that inverse-free abelian l-groups generate only a proper (infinitely based) subvariety of the variety of commutative distributive l-monoids\, b ut inverse-free l-groups generate the whole variety of distributive l-mono ids. We will also see that the validity of an l-group equation can be redu ced to the validity of a (constructible) finite set of l-monoid equations\ , yielding --- since the variety of distributive l-monoids has the finite model property — an alternative proof of the decidability of the equatio nal theory of l-groups.\n LOCATION:https://researchseminars.org/talk/OLS/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Riley Thornton (UCLA) DTSTART:20220324T180000Z DTEND:20220324T190000Z DTSTAMP:20260422T225801Z UID:OLS/89 DESCRIPTION:Title: An algebraic approach to Borel CSPs\nby Riley Thornton (UCLA) as part of Online logic seminar\n\n\nAbstract\nI will explain how some of the algebra ic tools behind the CSP dichotomy theorem in computer science can be adapt ed to answer questions in Borel combinatorics.\n LOCATION:https://researchseminars.org/talk/OLS/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Manlio Valenti (University of Udine) DTSTART:20220331T180000Z DTEND:20220331T190000Z DTSTAMP:20260422T225801Z UID:OLS/90 DESCRIPTION:Title: The first-order part of Weihrauch degrees\nby Manlio Valenti (University of Udine) as part of Online logic seminar\n\n\nAbstract\nGiven an order $( P\,\\le)$\, a natural strategy to prove that $a \\not\\le b$ is to present an example of some $c\\le a$ such that $c \\not\\le b$. Of course\, choos ing such a $c$ can be very challenging.\n\nIn the context of TTE and Weihr auch reducibility\, (Dzhafarov\, Solomon\, Yokoyama) introduced the notion of ``first-order part" of a computational problem $f$\, capturing the ``s trongest computational problem that is Weihrauch-below $f$". Characterizin g the first-order part of a given problem can be challenging as well\, but it proved to be a very useful tool\, especially when comparing principles that are (relatively) high in the Weihrauch hierarchy.\n\nIn this talk\, we will study the first-order part from a more algebraic perspective\, and study its relation with several other operators already defined in the li terature. We will then show how the obtained results can be used to easily characterize the first-order part of many known problems.\n LOCATION:https://researchseminars.org/talk/OLS/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Forte Shinko (Cal Tech) DTSTART:20220414T180000Z DTEND:20220414T190000Z DTSTAMP:20260422T225801Z UID:OLS/92 DESCRIPTION:Title: Rea lizations of equivalence relations and subshifts\nby Forte Shinko (Cal Tech) as part of Online logic seminar\n\n\nAbstract\nEvery continuous act ion of a countable group on a Polish space induces a Borel equivalence rel ation. We are interested in the problem of realizing (i.e. finding a Borel isomorphic copy of) these equivalence relations as continuous actions on compact spaces. We provide a number of positive results for variants of th is problem\, and we investigate the connection to subshifts.\n LOCATION:https://researchseminars.org/talk/OLS/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Ioannis Souldatos (Aristotle University of Thessaloniki) DTSTART:20220505T180000Z DTEND:20220505T190000Z DTSTAMP:20260422T225801Z UID:OLS/93 DESCRIPTION:Title: (No n)-Absolute Characterizations of Cardinals\nby Ioannis Souldatos (Aris totle University of Thessaloniki) as part of Online logic seminar\n\n\nAbs tract\nPDF Abstract Here\n LOCATION:https://researchseminars.org/talk/OLS/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Zaffora Blando (Carnegie Mellon University) DTSTART:20221215T190000Z DTEND:20221215T200000Z DTSTAMP:20260422T225801Z UID:OLS/94 DESCRIPTION:Title: Ran domness and Invariance\nby Francesca Zaffora Blando (Carnegie Mellon U niversity) as part of Online logic seminar\n\n\nAbstract\nThe first (semi- )formal definition of randomness for infinite binary sequences dates back to von Mises’ work in the foundations of probability and statistics . According to von Mises\, a sequence is random if\, within it\, the relat ive frequencies of 0 and 1 converge to a limit and these limiting relative frequencies are invariant under a class of transformations called selecti on rules. The randomness notion introduced by von Mises is nowadays widely regarded as being too weak and his account has been supplanted by the the ory of algorithmic randomness\, which characterizes randomness using the t ools of computability theory and measure theory. The goal of this talk is two-fold. First\, I will discuss a lesser-known characterization of Schnor r randomness due to Schnorr\, which demonstrates that it is possible to ob tain a satisfactory randomness notion by defining randomness\, analogously to how von Mises did it\, in terms of the invariance of limiting relative frequencies. Then\, I will discuss how other canonical algorithmic random ness notions are similarly characterizable in terms of the preservation of natural properties under the class of computable measure-preserving trans formations. This talk is based on joint work with Floris Persiau.\n LOCATION:https://researchseminars.org/talk/OLS/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Ramyaa (New Mexico Tech) DTSTART:20220818T180000Z DTEND:20220818T190000Z DTSTAMP:20260422T225801Z UID:OLS/95 DESCRIPTION:Title: Adv ances in Differentiable Program Learning\nby Ramyaa (New Mexico Tech) as part of Online logic seminar\n\n\nAbstract\nInductive Logic Programming (ILP) is a subfield of Artificial Intelligence that learns Logic Programs for a concept from positive and negative examples of the concept.\nLearni ng Logic Programs allow for interpretability\, can benefit from background knowledge\, and require small training set. However\, traditional ILP tec hniques are not noise-tolerant\, and do not scale well to large/high-dimen sional domains. In recent years\, there have been several attempts to use differentiable representations of logic programs and learn them using grad ient descent based techniques. This talk introduces these attempts\, and o ur efforts at extending them to learn logic programs with negations and hi gher-order logic programs.\n\nIn both cases\, considerable care is needed from a theoretical standpoint. Negation should be restricted to avoid para doxical scenarios. We learned logic programs with stratified negation (in the style of Datalog). Anti-unification (i.e.\, generalization) of arbitra ry higher-order terms is not unique. We learned second order logic program s that are generalizations of first order programs.\n LOCATION:https://researchseminars.org/talk/OLS/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Conant (The Ohio State University) DTSTART:20221027T180000Z DTEND:20221027T190000Z DTSTAMP:20260422T225801Z UID:OLS/96 DESCRIPTION:Title: Sep aration for isometric group actions and hyperimaginary independence\nb y Gabriel Conant (The Ohio State University) as part of Online logic semin ar\n\n\nAbstract\nIn the theory of (finite) permutation groups\, P. M. Neu mann’s Lemma says that if a group G acts on a set X\, and P is a finite subset of X such that all points of P have an infinite orbit\, then for an y other finite set in Q there is a group element g such that gP is disjoin t from Q. When applied to the automorphism group of a first-order structur e\, this lemma can be used to prove a number of useful results in model th eory. In this talk\, I will present a metric space version of P. M. Neumma n’s Lemma\, along with several applications in the model theory of metri c structures. For example\, we show that algebraic independence in continu ous logic satisfies the “full existence axiom”\, answering a question of Andrews\, Goldbring\, and Keisler. Time permitting\, I will also discus s some consequences for hyperimaginaries\, which are new even in classical discrete logic. Joint work with J. Hanson.\n LOCATION:https://researchseminars.org/talk/OLS/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Vidaux (Universidad de Concepción) DTSTART:20220825T180000Z DTEND:20220825T190000Z DTSTAMP:20260422T225801Z UID:OLS/97 DESCRIPTION:Title: Tow ers of totally real nested square roots: undecidability\, the lattice of s ubfields\, and the quartic extensions within the tower\nby Xavier Vida ux (Universidad de Concepción) as part of Online logic seminar\n\n\nAbstr act\nAfter recalling some first order undecidability results in infinite a lgebraic extensions of the field of rational numbers\, I will talk about a concrete family of 2-towers of totally real number fields\, namely\, $(\\ mathbb{Q}(x_n))_{n\\ge0}$\, where $x_{n+1}=\\sqrt{\\nu+x_n}$ for some give n positive integers $\\nu$ and $x_0$. Let $K$ be the union of the $\\mathb b{Q}(x_n)$. Though these fields $K$ are somewhat the simplest subfields of an algebraic closure of $\\mathbb{Q}$ that one may construct\, they hide a rich variety of natural problems of topological\, algebraic\, dynamical and logical nature. The results that I will present about these fields are due to M. Castillo\, C. Videla\, and who writes.\n LOCATION:https://researchseminars.org/talk/OLS/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Karen Lange (Wellesley College) DTSTART:20220901T180000Z DTEND:20220901T190000Z DTSTAMP:20260422T225801Z UID:OLS/99 DESCRIPTION:Title: Cla ssification via effective lists\nby Karen Lange (Wellesley College) as part of Online logic seminar\n\n\nAbstract\n"Classifying" a natural class of structures is a common goal in mathematics. Providing a classificati on can mean different things\, e.g.\, determining a set of invariants that settle the isomorphism problem or instead creating a list of all structur es of a given kind without repetition of isomorphism type. Here we discuss recent work on classifications of the latter kind from the perspective of computable structure theory. We’ll consider natural classes of comput able structures such as vector spaces\, equivalence relations\, algebraic fields\, and trees to better understand the nuances of classification via effective lists and its relationship to other forms of classification.\n LOCATION:https://researchseminars.org/talk/OLS/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Patricia Blanchette (University of Notre Dame) DTSTART:20220908T180000Z DTEND:20220908T190000Z DTSTAMP:20260422T225801Z UID:OLS/100 DESCRIPTION:Title: Fo rmalism in Logic\nby Patricia Blanchette (University of Notre Dame) as part of Online logic seminar\n\n\nAbstract\nLogic became ‘formal’ at the end of the 19th century primarily in pursuit of deductive rigor within mathematics. But by the early 20th century\, a formal treatment of logic had become essential to two new streams in the current of logic: the colle ction of crucial ‘semantic’ notions surrounding the idea of categorici ty\, and the project of examining the tools of logic themselves\, in the w ay that’s crucial for the treatment of completeness (in its various guis es). This lecture discusses the variety of different tasks that have been assigned the notion of formalization in the recent history of logic\, with an emphasis on some of the ways in which the distinct purposes of formali zation are not always in harmony with one another.\n LOCATION:https://researchseminars.org/talk/OLS/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Neer Bhardwaj (Weizmann Institute) DTSTART:20220915T180000Z DTEND:20220915T190000Z DTSTAMP:20260422T225801Z UID:OLS/101 DESCRIPTION:Title: An analytic AKE program with induced structure results on coefficient field and monomial group\nby Neer Bhardwaj (Weizmann Institute) as part of O nline logic seminar\n\n\nAbstract\nWe develop an extension theory for anal ytic valuation rings in order to establish Ax-Kochen-Ersov type results fo r these structures. New is that we can add in salient cases lifts of the r esidue field and the value group and show that the induced structure on th e lifted residue field is just its field structure\, and on the lifted val ue group is just its ordered abelian group structure. This restores an ana logy with the non-analytic AKE-setting that was missing in earlier treatme nts of analytic AKE-theory. Joint work with Lou van den Dries.\n LOCATION:https://researchseminars.org/talk/OLS/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Philip White (George Washington University) DTSTART:20221103T180000Z DTEND:20221103T190000Z DTSTAMP:20260422T225801Z UID:OLS/102 DESCRIPTION:Title: A Two-Cardinal Ramsey Operator on Ideals\nby Philip White (George Washin gton University) as part of Online logic seminar\n\n\nAbstract\nLet $I$ be a $\\kappa$-complete ideal on $\\kappa$. Similar to the one-cardinal inef fability operator of Baumgartner\, Feng defined a one-cardinal Ramsey oper ator on $I$. A basic result of Feng is applying the one cardinal Ramsey op erator to $I$ yields a normal ideal. Feng also showed under what condition s the ideal given by applying the Ramsey operator is equivalently generate d by a “pre-Ramsey” ideal as well as the $\\Pi^1_{n+1}$ indescribabili ty ideal. Finally Feng showed iterated use of the one-cardinal Ramsey ope rator forms a proper hierarchy. Feng was able to show these results for $< \\kappa+$ iterations of the one-cardinal Ramsey operator by utilizing can onical functions. Similar to other results of Brent Cody and the presenter \, these results in the one-cardinal setting can be generalized to a two-c ardinal setting. The theorems of Feng will be discussed in detail as well as the analogous two-cardinal versions of Brent Cody and the presenter.\n LOCATION:https://researchseminars.org/talk/OLS/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Protzenko (Microsoft Research) DTSTART:20221013T180000Z DTEND:20221013T190000Z DTSTAMP:20260422T225801Z UID:OLS/103 DESCRIPTION:Title: Co mputational Law: Programming Languages meet the Law\nby Jonathan Protz enko (Microsoft Research) as part of Online logic seminar\n\n\nAbstract\nM any parts of the law\, such as tax code\, pension computations\, etc. enco de a clear and unambiguous algorithm: they are called computational law. B ut ordinary citizens without legal counsel are oftentimes powerless\, beca use layers of legalese and opaque implementations obscure the underlying a lgorithm.\n\nThe Correct Computational Law project tackles this inequity b y formalizing and capturing computational law using formal methods. Whethe r it is the French Tax Code\, French family benefits or Washington State's Legal Financial Obligations\, we formalize\, re-implement and find bugs i n the law. Doing so\, we make it possible for ordinary citizens to prevail over the complexity of the law\, rather than falling prey to it.\n\nWe wi ll first describe our research agenda and ongoing efforts spanning France and the US. Then\, we will focus on a case study: the complexity of federa l civil procedure in the US\, and how the Lean proof assistant can always find\, with mathematical certainty\, a path through the pleading phase tha t fulfills all major procedural requirements.\n LOCATION:https://researchseminars.org/talk/OLS/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Kirsten Eisenträger (Penn State University) DTSTART:20221020T180000Z DTEND:20221020T190000Z DTSTAMP:20260422T225801Z UID:OLS/104 DESCRIPTION:Title: A topological approach to undefinability in algebraic extensions of the rati onals\nby Kirsten Eisenträger (Penn State University) as part of Onli ne logic seminar\n\n\nAbstract\nIn 1970 Matiyasevich proved that Hilbert ’s Tenth Problem over the\nintegers is undecidable\, building on work by Davis-Putnam-Robinson.\nHilbert’s Tenth Problem over the rationals is s till open\, but it could\nbe resolved by giving an existential definition of the integers inside\nthe rationals.\n\nProving whether such a definitio n exists is still out of reach. However\,\nwe will show that only “very few” algebraic extensions of the rationals\nhave the property that their ring of integers are existentially or\nuniversally definable. Equipping t he set of all algebraic extensions of\nthe rationals with a natural topolo gy\, we show that only a meager subset\nhas this property. An important t ool is a new normal form theorem for\nexistential definitions in such exte nsions. As a corollary\, we\nconstruct countably many distinct computable algebraic extensions whose\nrings of integers are neither existentially n or universally definable.\nJoint work with Russell Miller\, Caleb Springer \, and Linda Westrick.\n LOCATION:https://researchseminars.org/talk/OLS/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford University) DTSTART:20220922T180000Z DTEND:20220922T190000Z DTSTAMP:20260422T225801Z UID:OLS/105 DESCRIPTION:Title: Ra ndom walks and combinatorial dimensions in o-minimal groups\nby Hunter Spink (Stanford University) as part of Online logic seminar\n\n\nAbstract \nI will discuss some ideas that go into showing that $n$-independent-step random walks in o-minimally definable group over the real numbers (like a semi-algebraic group) has at most an $n^{-C}$ probability of finishing on a lower-dimensional target set unless the target set contains an ``expone ntial arc''\, where $C$ only depends on the dimension of the target set.\n LOCATION:https://researchseminars.org/talk/OLS/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Bagayoko (Université de Mons) DTSTART:20221110T190000Z DTEND:20221110T200000Z DTSTAMP:20260422T225801Z UID:OLS/106 DESCRIPTION:Title: So me ordered groups of generalized series\nby Vincent Bagayoko (Universi té de Mons) as part of Online logic seminar\n\n\nAbstract\nI will talk ab out some problems relating linearly ordered groups to logic and real geome try.\nI will show how to certain generalized series\, similar to transseri es\, in order to answer an open question regarding orderable groups.\n LOCATION:https://researchseminars.org/talk/OLS/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Csima (University of Waterloo) DTSTART:20221117T190000Z DTEND:20221117T200000Z DTSTAMP:20260422T225801Z UID:OLS/107 DESCRIPTION:Title: De grees of Categoricity\nby Barbara Csima (University of Waterloo) as pa rt of Online logic seminar\n\n\nAbstract\nA degree of categoricity is a Tu ring degree that exactly captures the complexity of computing isomorphisms between computable copies of some computable structure. In this talk I wi ll start by giving some easy examples of degrees of categoricity. I will t hen give a review of what is known about degrees of categoricity\, culmina ting in new results (joint work with Dino Rossegger).\n LOCATION:https://researchseminars.org/talk/OLS/107/ END:VEVENT BEGIN:VEVENT SUMMARY:David Schrittesser (University of Toronto) DTSTART:20221201T190000Z DTEND:20221201T200000Z DTSTAMP:20260422T225801Z UID:OLS/108 DESCRIPTION:Title: No nstandard analysis and statistical decision theory\nby David Schrittes ser (University of Toronto) as part of Online logic seminar\n\n\nAbstract\ nStatistical decision theory takes inspiration from game theory to provide a basic framework in which one can reason about optimality (or lack there of) of statistical procedures\, such as estimators and tests.\n\nOne prope rty of a statistical procedure is "admissibility": Roughly\, a procedure i s admissible if there is no other procedure which does better under all ci rcumstances ("better" in a sense specified by the decision theoretical fra mework\, i.e.\, with respect to a fixed loss function). This is certainly a necessary condition for optimality.\n\nAdmissibility is notoriously hard to characterize. In particular\, establishing a characterization in Bayes ian terms has been an ongoing pursuit for decades in statistical decision theory. Recently we have found a characterization of admissibility in Baye sian terms\, by using prior probability distributions which can take on in finitesimal values. We are also able to draw connections to classical meth ods establishing admissibility\, such as Blyth's method and Stein's charac terization of admissibility (which does partially characterize admissibili ty\, but only under additional\, technical hypotheses). Finally\, our meth od has applications in concrete problems such as the problem of establishi ng the admissibility of the Graybill-Deal estimator.\n\nThe talk will not presuppose any knowledge on statistics or nonstandard analysis. Everything is joint work with D. Roy and H. Duanmu.\n LOCATION:https://researchseminars.org/talk/OLS/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Patrick Lutz (UCLA) DTSTART:20230119T190000Z DTEND:20230119T200000Z DTSTAMP:20260422T225801Z UID:OLS/109 DESCRIPTION:Title: Th e Solecki dichotomy and the Posner Robinson theorem\nby Patrick Lutz ( UCLA) as part of Online logic seminar\n\n\nAbstract\nThe Solecki dichotomy in descriptive set theory\, roughly stated\, says that every Borel functi on on the real numbers is either a countable union of partial continuous f unctions or at least as complicated as the Turing jump. The Posner-Robinso n theorem in computability theory\, again roughly stated\, says that every non-computable real looks like 0' relative to some oracle. Superficially\ , these theorems look similar: both roughly say that some object is either simple or as complicated as the jump. However\, it is not immediately app arent whether this similarity is more than superficial. If nothing else\, the Solecki dichotomy is about third order objects—functions on the real numbers—while the Posner-Robinson theorem is about second order objects —individual real numbers. We will show that there is a genuine mathemati cal connection between the two theorems by showing that the Posner-Robinso n theorem plus determinacy can be used to give a short proof of a slightly weakened version of the Solecki dichotomy\, and vice-versa.\n LOCATION:https://researchseminars.org/talk/OLS/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Hrušák (Universidad Nacional Autónoma de México) DTSTART:20230216T190000Z DTEND:20230216T200000Z DTSTAMP:20260422T225801Z UID:OLS/110 DESCRIPTION:Title: Mo del theory and topological groups\nby Michael Hrušák (Universidad Na cional Autónoma de México) as part of Online logic seminar\n\n\nAbstract \nWe shall discuss some recent applications of model-theoretic methods to the study of topological groups. In particular\, we shall discuss solution s to old problems of Comfort and van Douwen and the use of Fraissé theory to the study of groups of homeomorphisms.\n LOCATION:https://researchseminars.org/talk/OLS/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Maribel Fernandez (Kings College London) DTSTART:20230202T190000Z DTEND:20230202T200000Z DTSTAMP:20260422T225801Z UID:OLS/111 DESCRIPTION:Title: No minal Techniques for the Specification of Languages with Binders\nby M aribel Fernandez (Kings College London) as part of Online logic seminar\n\ n\nAbstract\nThe nominal approach to the specification of languages with b inding operators\, introduced by Gabbay and Pitts\, has its roots in nomin al set theory. Nominal logic is a theory of first-order logic that axiomat izes the notions of fresh name\, name swapping and abstraction from nomina l sets\, making it an ideal tool for the specification of the semantics of programming languages. In this talk\, we will start by recalling the main concepts of nominal logic\, and then we will show how to apply these idea s to specify calculi with binders. More precisely\, we will introduce nomi nal syntax (including the notions of fresh atoms and alpha-equivalence)\, present matching and unification algorithms that take into account the alp ha-equivalence relation\, define nominal rewriting (a generalisation of fi rst-order rewriting that provides in-built support for alpha-equivalence f ollowing the nominal approach) and give examples of application.\n LOCATION:https://researchseminars.org/talk/OLS/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Adele Padgett (McMaster University) DTSTART:20230126T190000Z DTEND:20230126T200000Z DTSTAMP:20260422T225801Z UID:OLS/112 DESCRIPTION:Title: Re gular solutions of systems of transexponential polynomials\nby Adele P adgett (McMaster University) as part of Online logic seminar\n\n\nAbstract \nI will explain an open problem in the model theory of ordered fields and outline a possible strategy for resolving it. The problem is whether ther e are o-minimal fields that are “transexponential”\, i.e.\, which defi ne functions that eventually grow faster than any tower of exponentials. I n recent work\, I gave evidence indicating that a particular transexponent ial expansion of the real field might be o-minimal. A possible next step w ould be to apply a criterion of Lion which grew out of Wilkie’s proof th at the real exponential field is o-minimal.\n LOCATION:https://researchseminars.org/talk/OLS/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Konstantin Slutsky (Iowa State University) DTSTART:20230302T190000Z DTEND:20230302T200000Z DTSTAMP:20260422T225801Z UID:OLS/114 DESCRIPTION:Title: Pa rtial actions and orbit equivalence relations\nby Konstantin Slutsky ( Iowa State University) as part of Online logic seminar\n\n\nAbstract\nIn t his talk\, we will discuss the framework of partial actions\nfor construct ing orbit equivalent actions of Polish groups. While\nrelated ideas have b een employed in ergodic theory and Borel\ndynamics for many years\, the pa rticular viewpoint of partial\nactions simplifies construction of orbit eq uivalent actions\nof distinct groups. \n\nAs an application\, we will pre sent a Borel version of Katok's\nrepresentation theorem for multidimension al Borel\nflows. One-dimensional flows are closely connected to actions\no f $\\mathbb{Z}$ via the so-called "flow under a function"\nconstruction. This appealing geometric picture does not\ngeneralize to higher dimensions . Within the ergodic theoretical\nframework\, Katok introduced the concep t of a special flow as a\nway to connect multidimensional $\\mathbb{R}^d$ and $\\mathbb{Z}^d$\nactions. We will show that similar connections conti nue to hold\nin Borel dynamics.\n\nAnother illustration of the partial act ions techniques that we\nintend to touch is the following result: a Borel equivalence\nrelation generated by a free R-flow can also be generated by a\nfree action of any non-discrete and non-compact Polish\ngroup. This is in contrast with the situation for discrete\ngroups\, where amenability di stinguishes groups that can and\ncannot generate free finite measure-prese rving hyperfinite actions.\n LOCATION:https://researchseminars.org/talk/OLS/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Athar Abdul-Quader (Purchase College) DTSTART:20230323T180000Z DTEND:20230323T190000Z DTSTAMP:20260422T225801Z UID:OLS/115 DESCRIPTION:Title: Ar ithmetic Saturation and Pathological Satisfaction\nby Athar Abdul-Quad er (Purchase College) as part of Online logic seminar\n\n\nAbstract\nA cla ssic result in models of arithmetic states that countable models of PA are recursively saturated if and only if they possess a "full satisfaction cl ass". A satisfaction class is a set of pairs (phi\, alpha)\, where phi is a code for a formula in the sense of the model\, and alpha is an assignmen t for that formula\, which extends the "standard" satisfaction relation\, and satisfies Tarksi's compositional rules for satisfaction. Recently\, th ere has been work on so-called pathological satisfaction classes: satisfac tion classes which exhibit certain pathologies\, like\, for example\, maki ng sentences of the form "(0 = 1) or (0 = 1) or ... or (0 =1)" of nonstand ard length true. We study these pathologies\, and find a surprising relati onship between the question of determining which sets can be defined using certain pathologies\, and a stronger notion of saturation\, arithmetic sa turation. This is joint work with Mateusz Łełyk\, based heavily on unpub lished work by Jim Schmerl.\n LOCATION:https://researchseminars.org/talk/OLS/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Mourad (University of Connecticut) DTSTART:20230504T180000Z DTEND:20230504T190000Z DTSTAMP:20260422T225801Z UID:OLS/116 DESCRIPTION:Title: Co mputing Non-Repetitive Sequences Using the Lovász Local Lemma\nby Da niel Mourad (University of Connecticut) as part of Online logic seminar\n\ n\nAbstract\nWe discuss effective versions of classical results on the exi stence of non-repetitive sequences first proven using the Lovász Local Le mma\, a non-constructive existence result from the probabilistic method. W e outline the path to these constructions. First\, a probabilistic resampl e algorithm converges to a witness to the Local Lemma in polynomial expect ed time. Then\, the bound on the expectation is used to build a determinis tic algorithm with computable convergence time. However\, the resulting ef fective computation has constraints that make it unsuitable for constructi ng non-repetitive sequences. We modify the resample algorithm and show tha t these modifications allow us to relax these constraints\n LOCATION:https://researchseminars.org/talk/OLS/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Jenna Zomback (Williams College) DTSTART:20230316T180000Z DTEND:20230316T190000Z DTSTAMP:20260422T225801Z UID:OLS/117 DESCRIPTION:Title: We ak mixing for semigroup actions and applications to pointwise ergodic theo rems\nby Jenna Zomback (Williams College) as part of Online logic semi nar\n\n\nAbstract\nWe provide a sufficient condition for the natural bound ary action of free semigroups to be weak mixing. This result yields new po intwise ergodic theorems for free semigroup actions\, where the averages a re taken along trees. This is joint work with Anush Tserunyan.\n LOCATION:https://researchseminars.org/talk/OLS/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Liling Ko (Ohio State University) DTSTART:20230209T190000Z DTEND:20230209T200000Z DTSTAMP:20260422T225801Z UID:OLS/118 DESCRIPTION:Title: Co mputable smallness is not intrinsic smallness\nby Liling Ko (Ohio Stat e University) as part of Online logic seminar\n\n\nAbstract\nWe construct a set $A$ that is computably small but not intrinsically small. To underst and these terms\, we liken $A$ to a game show host playing against a class of computable contestants\, analogous to an infinite variant of the Monty Hall problem. The host has infinitely many doors arranged in a line\, and each door hides either a goat or a car. A contestant selects infinitely m any doors to open and wins if a non-zero density of the selected doors hid es a car. Contestants that are disorderly can select doors out of order\, opening door $i$ after door $j>i$. Are disorderly contestants more difficu lt to beat than orderly ones? This is known to be true if contestants are allowed to be adaptive\, where they may choose a different door depending on the outcomes of the previously opened ones [1] (via the theorem that MW C-stochasticity 0 does not imply Kolmogorov-Loveland-stochasticity 0). We give a constructive proof to show that the statement also holds in the non -adaptive setting\, shedding light on a disorderly structure that outperfo rms orderly ones. This is joint work with Justin Miller.\n\n[1] Merkle\, W olfgang and Miller\, Joseph S and Nies\, Andre and Reimann\, Jan and Steph an\, Frank. Kolmogorov--Loveland randomness and stochasticity. Annals of P ure and Applied Logic\, vol.138 (2006)\, no.1-3\, pp.183--210.\n LOCATION:https://researchseminars.org/talk/OLS/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Cian Dorr (New York University) DTSTART:20230427T180000Z DTEND:20230427T190000Z DTSTAMP:20260422T225801Z UID:OLS/119 DESCRIPTION:Title: No n-Extensional Higher Order Logic with Substitution\nby Cian Dorr (New York University) as part of Online logic seminar\n\n\nAbstract\nThe most w idely studied systems of classical higher-order logic are ‘extensional ’ in the sense that they validate the schema ∀x₁…xₙ(Fx₁…xₙ ↔Gx₁…xₙ) → (F=G): intuitively\, this means that they coextensive properties or relations are identical. Although this seems philosophical ly suspect for obvious reasons\, the space of logics that keep the classic al laws for propositional connectives and quantifiers while dropping exten sionality has been surprisingly little explored. This talk will explore a natural way of weakening extensionality by replacing it with the rule ⊦ Fx₁…xₙ↔Gx₁…xₙ / ⊦F=G\, or equivalently\, a rule that allow s provably materially equivalent formulae to be intersubstituted anywhere. I will give several very different axiomatizations of this system\, ther eby cementing the case for its naturalness. After that I will discuss a r ange of possible extensions of the system\, some of which restore certain arguably attractive consequences of extensionality\, and others of which t ake the view in a more “fine-grained” direction by systematically addi ng claims of non-identity which the basic system leaves unsettled. Finall y\, I will describe a technique for constructing set-theoretic models of t he system\, which can be used to prove the consistency of many of the afor ementioned extensions. \n\nThe talk will be based on a forthcoming paper coauthored with Andrew Bacon\, available here: https://philarchive.org/rec /BACC-8.\n LOCATION:https://researchseminars.org/talk/OLS/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandra Müller (TU Wien) DTSTART:20230406T180000Z DTEND:20230406T190000Z DTSTAMP:20260422T225801Z UID:OLS/120 DESCRIPTION:Title: Ca nonical Models of Determinacy\nby Sandra Müller (TU Wien) as part of Online logic seminar\n\n\nAbstract\nWoodin proved that every model of $\\m athsf{AD}^+$ (a natural strengthening of determinacy) is elementarily equi valent to a derived model. In joint work with Sargsyan\, we established a useful derived model representation for the Sealing model. In this talk\, I will outline this result (assuming no knowledge of inner model theory) a nd describe its relevance for the inner model program.\n LOCATION:https://researchseminars.org/talk/OLS/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Soskova (Sofia University St. Kliment Ohridski) DTSTART:20230223T190000Z DTEND:20230223T200000Z DTSTAMP:20260422T225801Z UID:OLS/121 DESCRIPTION:Title: Co hesive Powers of Linear Orders\nby Alexandra Soskova (Sofia University St. Kliment Ohridski) as part of Online logic seminar\n\n\nAbstract\nCohe sive powers of computable structures are effective analogs of ultrapowers\ , where cohesive sets play the role of ultrafilters. The aim is also to co mpare and contrast properties of cohesive powers with those of classical\n ultrapowers. Classically\, an ultrapower of a structure is elementarily eq uivalent to the base structure by\nŁ\;oś\;'s theorem. Effectively\ , Ł\;oś\;'s theorem holds for cohesive powers of decidable struc tures. For cohesive powers of $n$-decidable structures\, Ł\;oś\;' s theorem need only\nhold up to $\\Delta_{n+3}$-expressible sentences. In fact\, every $\\Sigma_{n+3}$ sentence true of an $n$-decidable\nstructure is also true of all of its cohesive powers\, but this is optimal in gener al. Classically\, ultrapowers of isomorphic structures over a fixed ultraf ilter are isomorphic. Effectively\,\ncohesive powers of computably isomorp hic computable structures over a fixed cohesive\nset are isomorphic. Howev er\, it is possible for isomorphic (but not computably\nisomorphic) comput able structures to have non-elementarily equivalent (hence non-isomorphic) \ncohesive powers. Classically\, the Keisler–Shelah theorem states that two structures are elementarily equivalent if\nand only if there is an ult rafilter over which the corresponding\nultrapowers are isomorphic. Effecti vely\, an analogous result holds for decidable structures.\nIf the structu res are computable that are not necessarily decidable\, then the\neffectiv e version of the Keisler–Shelah theorem can fail in either direction. Cl assically\, for a countable language\, ultrapowers over countably incomple te ultrafilters are $\\aleph_1$-saturated. Effectively\, cohesive powers o f decidable structures are recursively saturated. Furthermore\, cohesive p owers of n-decidable structures are $\\Sigma_n$-recursively saturated. Mos t interestingly\, if the cohesive set is assumed to be co-c.e.\, then we o btain an additional level of saturation: cohesive powers of n-decidable st ructures over co-c.e.\ncohesive sets are $\\Sigma_{n+1}$-recursively satur ated.\n\n\nWe investigate the cohesive powers of computable linear orders\ , with special emphasis on computable copies of $\\omega$. If $\\mathcal{ L}$ is a computable copy of $\\omega$ that is computably isomorphic to the standard presentation of $\\omega$\, then every cohesive power of $\\math cal{L}$ has order-type $\\omega + \\zeta\\eta$. However\, there are compu table copies of $\\omega$\, necessarily not computably isomorphic to the s tandard presentation\, having cohesive powers not elementarily equivalent to $\\omega + \\zeta\\eta$. For example\, we show that there is a computa ble copy of $\\omega$ with a cohesive power of order-type $\\omega + \\eta $. Our most general result is that if $X \\subseteq \\mathbb N \\setminus \\{0\\}$ is a Boolean combination of $\\Sigma_2$ sets\, thought of as a set of finite order-types\, then there is a computable copy of $\\omega$ w ith a cohesive power of order-type $\\omega + \\bm{\\sigma}(X \\cup \\{\\o mega + \\zeta\\eta + \\omega^*\\})$\, where $\\bm{\\sigma}(X \\cup \\{\\om ega + \\zeta\\eta + \\omega^*\\})$ denotes the shuffle of the order-types in $X$ and the order-type $\\omega + \\zeta\\eta + \\omega^*$. Furthermor e\, if $X$ is finite and non-empty\, then there is a computable copy of $\ \omega$ with a cohesive power of order-type $\\omega + \\bm{\\sigma}(X)$.\ n\nThis is a joint work with Rumen Dimitrov\, Valentina Harizanov\, Andrey Morozov\, Paul Shafer and Stefan Vatev.\n\nIt was partially supported b y Bulgarian National Science Fund KP-06-Austria-04/06.08.2019\,\nFNI-SU 80 -10-134/20.05.2022.\n LOCATION:https://researchseminars.org/talk/OLS/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Una Stojnić (Princeton University) DTSTART:20230511T180000Z DTEND:20230511T190000Z DTSTAMP:20260422T225801Z UID:OLS/123 DESCRIPTION:by Una Stojnić (Princeton University) as part of Online logic seminar\n\n\nAbstract\nInferential Constraint and If φ ought φ Problem\ n\n \n\nThe standard semantics for modality\, together with the influentia l restrictor analysis of conditionals (Kratzer 1986\; 2012) validates cond itional constructions of the form ⌜φ$\\rightarrow$ □φ⌝. This is ba d news\; constructions like (1) aren’t intuitively trivially true:\n\n \ n\n1. If John's stealing\, he ought to be stealing.\n\n \n\nWhile this mig ht seem like a problem specifically for the restrictor analysis of conditi onals\, the issue is far more general. For any account must predict that m odals in the consequent sometimes receive obligatorily unrestricted interp retation\, as in (1)\, but sometimes appear restricted\, as in (2):\n\n \n \n2. If John's speeding\, he ought to pay the fine.\n\n \n\nAnd the proble m runs deeper\, for there are non-conditional variants of the problematic data. Thus\, the solution cannot lie in adopting a particular analysis of conditionals\, nor a specific account of the interaction between condition als and modals. Indeed\, with minimal assumptions\, the standard account o f modality will render a massive number of claims about what one ought to\ , must\, or may\, do trivially true. Worse\, the problem extends to a wide range of non-deontic modalities\, including metaphysical modality. But th e disaster has a remedy. I argue that the source of the problem lies in th e standard account’s failure to capture an inferential evidence constrai nt encoded in the meaning of a wide range of modal constructions. I offer a semantic account that captures this constraint\, and show it provides a general and independently motivated solution to the problem\, avoiding unw anted validities.\n LOCATION:https://researchseminars.org/talk/OLS/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Elliot Kaplan (McMaster University) DTSTART:20230330T180000Z DTEND:20230330T190000Z DTSTAMP:20260422T225801Z UID:OLS/124 DESCRIPTION:Title: Hi lbert polynomials for finitary matroids\nby Elliot Kaplan (McMaster Un iversity) as part of Online logic seminar\n\n\nAbstract\nEventual polynomi al growth is a common theme in combinatorics and commutative algebra. The quintessential example of this phenomenon is the Hilbert polynomial\, whic h eventually coincides with the linear dimension of the graded pieces of a finitely generated module over a polynomial ring. A later result of Kolch in shows that the transcendence degree of certain field extensions of a di fferential field is eventually polynomial. More recently\, Khovanskii show ed that for finite subsets A and B of a commutative semigroup\, the size o f the sumset A+tB is eventually polynomial in t. I will present a common g eneralization of these three results in terms of finitary matroids (also c alled pregeometries). I’ll discuss other instances of eventual polynomia l growth (like the Betti numbers of a simplicial complex) as well as some applications to bounding model-theoretic ranks. This is joint work with An tongiulio Fornasiero.\n LOCATION:https://researchseminars.org/talk/OLS/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Michaël Cadilhac (DePaul University) DTSTART:20230914T180000Z DTEND:20230914T190000Z DTSTAMP:20260422T225801Z UID:OLS/126 DESCRIPTION:Title: Ci rcuit Complexity as a Mathematician's Playground: Logic\, Algebra\, Combin atorics\nby Michaël Cadilhac (DePaul University) as part of Online lo gic seminar\n\n\nAbstract\nA (Boolean) circuit is a directed acyclic graph with AND\, OR\, and NOT nodes\, some input nodes\, and an output node\; t hey naturally compute Boolean functions. Circuit complexity is the study of how intricate or large a circuit needs to be in order to implement a gi ven Boolean function. If this description naturally hints to the use of c ombinatorial tools\, circuit complexity also relies on finite model theory and deep algebraic concepts — specifically\, (profinite) semigroup theo ry. In this talk\, I will focus on a specific class of circuits\, depth-3 circuits\, and will explore a class of "simple" Boolean functions they ex press. In doing so\, I will go on a guided tour of the logical\, algebrai c\, and combinatorial tools used in circuit complexity.\n\nBased on joint work with Corentin Barloy & Charles Paperman (U. Lille\, France) and Thoma s Zeume (Bochum U.\, Germany).\n LOCATION:https://researchseminars.org/talk/OLS/126/ END:VEVENT BEGIN:VEVENT SUMMARY:(Cancelled) DTSTART:20231102T180000Z DTEND:20231102T190000Z DTSTAMP:20260422T225801Z UID:OLS/127 DESCRIPTION:Title: (C ancelled due to speaker illness\; will reschedule)\nby (Cancelled) as part of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/OLS/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Kameryn Williams (Bard College at Simon's Rock) DTSTART:20231005T180000Z DTEND:20231005T190000Z DTSTAMP:20260422T225801Z UID:OLS/128 DESCRIPTION:Title: In terpretations and bi-interpretations in second-order arithmetic\nby Ka meryn Williams (Bard College at Simon's Rock) as part of Online logic semi nar\n\n\nAbstract\nThe property of tightness\, introduced by Visser\, give s a notion of semantic completeness for a theory. Specifically\, a theory T is tight if any two distinct extensions of T cannot be bi-interpretable. Important foundational theories like PA and ZF are tight. Consequently in terpretations of extensions of these theories must lose information. For e xample\, ZF + ¬AC can interpret ZFC by restricting to the constructible u niverse while ZFC can interpret ZF + ¬AC via\, essentially\, forcing. But these interpretations destroy information about the original universe\, a nd the tightness of ZF implies there are no alternative interpretations wh ich avoid this problem.\n\nEnayat asked whether the full strength of theor ies like ZF or full second-order arithmetic is necessary for the tightness results and conjectured that this property can be used to give a characte rization of these theories. Phrased in the contrapositive: must it be that any strict subtheory of these theories admits distinct\, bi-interpretable extensions? Alfredo Roque Freire and I investigated this question for sub systems of second-order arithmetic\, providing some evidence for Enayat’ s conjecture. We showed that if you restrict the comprehension axiom to fo rmulae of a bounded complexity then you can find two distinct yet bi-inter pretable extensions of the theory. The main idea of the construction\, not uncommon for work in logic\, goes back to an old observation by Mostowski . Namely\, while truth is not arithmetically definable\, it is definable o ver the arithmetical sets.\n LOCATION:https://researchseminars.org/talk/OLS/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Salma Kuhlmann (Universität Konstanz) DTSTART:20231026T180000Z DTEND:20231026T190000Z DTSTAMP:20260422T225801Z UID:OLS/129 DESCRIPTION:Title: Th e automorphism group of Hahn fields\nby Salma Kuhlmann (Universität K onstanz) as part of Online logic seminar\n\n\nAbstract\nSee abstract on se minar web page.\n LOCATION:https://researchseminars.org/talk/OLS/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Landon Elkind (Western Kentucky University) DTSTART:20231207T190000Z DTEND:20231207T200000Z DTSTAMP:20260422T225801Z UID:OLS/130 DESCRIPTION:Title: Pr incipia Mathematica\, Negative Types\, and a theorem of infinity for Z-Pri ncipia Mathematica\nby Landon Elkind (Western Kentucky University) as part of Online logic seminar\n\n\nAbstract\nI here develop a new\, foundat ionless simple-type grammar to replace Principia Mathematica's well-founde d simple-type grammar. Rewriting the axiom schemata of Principia in founda tionless simple-types\, or Z-types\, gives us a new system\, ZPM. Adding t o ZPM a plausible new axiom schema\, Z*107\, allows us prove Infinity in e very type. Z*107 is a plausible new axiom schema because\, as I will argue \, it is a logical truth of ZPM. Further\, using Z*107 to prove Infinity i s not circular: the new axiom alone does not secure a proof of Infinity\, but crucially relies on heterogeneous relations. So using Z*107 to prove I nfinity is not question-begging. In this talk I also relate this system to earlier discussions of Wang's Negative Types (and its extension by Specke r's TA).\n LOCATION:https://researchseminars.org/talk/OLS/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabella Scott (University of Chicago) DTSTART:20230824T180000Z DTEND:20230824T190000Z DTSTAMP:20260422T225801Z UID:OLS/131 DESCRIPTION:Title: Ef fective constructions of existentially closed groups\nby Isabella Scot t (University of Chicago) as part of Online logic seminar\n\n\nAbstract\nE xistentially closed groups were introduced in 1951 by group theorists\, in analogue with algebraically closed fields. Since then\, they have been f urther studied by Neumann\, Macintyre\, and Ziegler\, who elucidated deep connections with model theory and computability theory. We review some of the literature on existentially closed groups and present new results tha t further refine these connections. In particular we find a divergence be tween local and global complexity not visible from a purely algebraic stan dpoint.\n LOCATION:https://researchseminars.org/talk/OLS/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Timothy Trujillo (Sam Houston State University) DTSTART:20230907T180000Z DTEND:20230907T190000Z DTSTAMP:20260422T225801Z UID:OLS/132 DESCRIPTION:Title: No nstandard Methods in Topological Ramsey Theory: Revisiting the Nash-Willia ms Theorem\nby Timothy Trujillo (Sam Houston State University) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, we explore the appl ication of nonstandard methods within the framework of topological Ramsey theory. Central to our discussion is a nonstandard proof of the Nash-Willi ams theorem. We further investigate the potential of extending both the pr oof and the theorem's results to the abstract setting of topological Ramse y theory\, culminating in an examination of the abstract Nash-Williams the orem. Our aim is to offer an alternative perspective on well-established r esults\, highlighting the intersections between nonstandard techniques and topological Ramsey theory.\n LOCATION:https://researchseminars.org/talk/OLS/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Darío García (Universidad de los Andes) DTSTART:20230921T180000Z DTEND:20230921T190000Z DTSTAMP:20260422T225801Z UID:OLS/133 DESCRIPTION:Title: Ps eudofiniteness and measurability of the everywhere infinite forest\nby Darío García (Universidad de los Andes) as part of Online logic seminar \n\n\nAbstract\nA structure M is said to be pseudofinite if every first-or der sentence that is true in M has a finite model\, or equivalently\, if M is elementarily equivalent to an ultraproduct of finite structures. For t his kind of structures\, the fundamental theorem of ultraproducts ( Los' T heorem) provides a powerful connection between finite and infinite sets\, which can sometimes be used to prove qualitative properties of large finit e structures using combinatorial methods applied to non-standard cardinali ties of definable sets.\n\nThe concept of measurable structures was define d by Macpherson and Steinhorn in [2] as a method to study infinite structu res with strong conditions of finiteness and definability for the sizes of definable sets. The most notable examples are the ultraproducts of asympt otic classes of finite structures (e.g.\, the class of finite fields or th e class of finite cyclic groups). Measurable structures are supersimple of finite SU-rank\, but recent generalizations of this concept are more flex ible and allow the presence of structures whose SU-rank is possibly infini te.\n\nThe everywhere infinite forest is the theory of an acyclic graph G such that every vertex has infinite degree. It is a well-known example of an omega-stable theory of infinite rank. In this talk we will take this st ructure as a motivating example to introduce all the concepts mentioned ab ove\, showing that it is pseudofinite and giving a precise description of the sizes of their definable sets. In particular\, these results provide a description of forking and U-rank for the infinite everywhere forest in t erms of certain pseudofinite dimensions\, and also show that it is a gener alized measurable structure that can be presented as the ultraproduct of a multidimensional exact class of finite graphs. These results are joint wo rk with Melissa Robles\, and can be found in [1].\n\nReferences:\n\n[1] Da río García and Melissa Robles. Pseudofiniteness and measurability of the everywhere infinite forest. Available at arXiv: https://arxiv.org/pdf/230 9.00991.pdf\n\n[2] Dugald Macpherson and Charles Steinhorn. One-dimensiona l asymptotic classes of finite structures\, Transactions of the American M athematical Society\, vol. 360 (2008)\n LOCATION:https://researchseminars.org/talk/OLS/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Dino Rossegger (Technische Universität Wien) DTSTART:20231019T180000Z DTEND:20231019T190000Z DTSTAMP:20260422T225801Z UID:OLS/134 DESCRIPTION:Title: Le arning equivalence relations\nby Dino Rossegger (Technische Universit ät Wien) as part of Online logic seminar\n\n\nAbstract\nWhat does it mean for an equivalence relation on a Polish space to be\nlearnable? Motivated by the recent work of Fokina\, Kötzing\, and San\nMauro\, who formulated a framework to learn the isomorphism relation on\ncountable classes of st ructures\, we introduce frameworks that aim to\ngive a formal notion of le arnability for equivalence relations on Polish\nspaces. Our main results c haracterize learnability in these frameworks\nvia the descriptive complexi ty of the equivalence relations\, and\, using\ntechniques from higher recu rsion theory and effective descriptive set\ntheory\, we calculate the comp lexity of the class of learnable\nequivalence relations. At last\, we disc uss the learnability of\nequivalence relations arising naturally in comput ability theory.\nThis is joint work with Ted Slaman and Tomasz Steifer.\n LOCATION:https://researchseminars.org/talk/OLS/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Assaf Shani (Concordia University\, Montreal) DTSTART:20231109T190000Z DTEND:20231109T200000Z DTSTAMP:20260422T225801Z UID:OLS/135 DESCRIPTION:Title: Ge neric analysis of Borel homomorphisms for the finite Friedman-Stanley jump s\nby Assaf Shani (Concordia University\, Montreal) as part of Online logic seminar\n\n\nAbstract\nThe talk will begin by discussing the basic d efinitions and general goals behind the theory of Borel equivalence relati ons. We will focus on the Friedman-Stanley jumps =+n\, for n=1\,2\,... and n=ω. These Borel equivalence relations represent the notions of being cl assifiable using invariants which are countable sets of reals\, countable sets of countable sets of reals\, and so on. We consider the problem of co nstructing a Borel reduction from =+n to some other equivalence relation. For n=1 the situation is well understood and there are many such results. We present a technique for finding such a reduction when n>1\, based on Ba ire-category analysis of all Borel homomorphisms from =+n.\n LOCATION:https://researchseminars.org/talk/OLS/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Teresa Kouri Kissel (Old Dominion University) DTSTART:20230928T180000Z DTEND:20230928T190000Z DTSTAMP:20260422T225801Z UID:OLS/136 DESCRIPTION:Title: Pr oof-Theoretic Pluralism and Harmony\nby Teresa Kouri Kissel (Old Domin ion University) as part of Online logic seminar\n\n\nAbstract\nAbstract: F errari and Orlandelli (2019) propose that an admissibility condition on a proof-theoretic logical pluralism be that the logics in question must be h armonious\, in the sense of Belnap (1962). This means that they must have connectives which are unique and conservative. This allows them to develop an innovative pluralism\, which shows variance on two levels. On one leve l\, we have a pluralism at the level of validity alone\, like that in Rest all (2014). But\, thanks to the Ferrari and Orlandelli system\, which was developed in response to some concerns of Kouri (2016)\, we can add a seco nd level and admit some logics which do not share connective meanings\, an d hence have different operational rules. This allows for us to have a plu ralism at two levels: the level of validity and the level of connective me anings.\n\nHere\, I will show that we can extend the system one step furth er\, and induce a three-level logical pluralism. The first and second leve ls remain as suggested by Ferrari and Orlandelli (2019)\, but we can allow for multiple notions of uniqueness in the definition of Belnap-harmony\, or multiple notions of harmony writ large. Either of these options generat es a pluralism at the level of our admissibility conditions. This generate s a pluralism at three levels: validity\, connective meanings\, and admiss ibility conditions. But it still preserves the spirit of the Ferrari and O rlandelli (2019) solution: harmony remains as the admissibility constraint across the board\, and so the original worries of Kouri (2016) are still put to rest and the original Beall and Restall (2006) criteria for admissi ble logics are still met.\n LOCATION:https://researchseminars.org/talk/OLS/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Canceled DTSTART:20231116T190000Z DTEND:20231116T200000Z DTSTAMP:20260422T225801Z UID:OLS/137 DESCRIPTION:by Canceled as part of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/OLS/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Diana Carolina Montoya (Technische Universität Wien) DTSTART:20231130T190000Z DTEND:20231130T200000Z DTSTAMP:20260422T225801Z UID:OLS/138 DESCRIPTION:Title: Ca rdinal characteristics and singular cardinals\nby Diana Carolina Monto ya (Technische Universität Wien) as part of Online logic seminar\n\n\nAbs tract\nThroughout the last few years\, many generalizations from classical cardinal characteristics of the Baire space have been studied. Special in terest has been given to the study of the combinatorics of the generalized Baire spaces $\\kappa^\\kappa$ when $\\kappa$ is an uncountable regular c ardinal (or even a large cardinal) but lately\, the generalization to sing ular cardinals has also been the focus of interest. In this talk\, I will present first the motivation within Set Theory to study these kinds of que stions and afterward some results regarding a generalization to the contex t of singular cardinals of the concepts of maximal almost disjoint and max imal independence families and point out the differences concerning the re gular case. Finally\, I will mention the open questions and possible futur e research paths in this area.\n LOCATION:https://researchseminars.org/talk/OLS/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicholas Ramsey (University of Notre Dame) DTSTART:20231214T190000Z DTEND:20231214T200000Z DTSTAMP:20260422T225801Z UID:OLS/139 DESCRIPTION:Title: Mo del theory and the Lazard Correspondence\nby Nicholas Ramsey (Universi ty of Notre Dame) as part of Online logic seminar\n\n\nAbstract\nThe Lazar d Correspondence is a characteristic $p$ analogue of the correspondence be tween nilpotent Lie groups and Lie algebras\, associating to every nilpote nt group of exponent $p$ and nilpotence class $c$ a Lie algebra over $F_p$ with the same nilpotence class (assuming $c < p$). We will describe the r ole that this translation between nilpotent group theory and linear algebr a has played in an emerging program to understand the first order properti es of random nilpotent groups. In this talk\, we will focus on connection s to neostability theory\, highlighting the way that nilpotent groups furn ish natural algebraic structures in surprising parts of the SOP$_n$ and $n $-dependence hierarchies. This is joint work with Christian d'Elbée\, Is abel Müller\, and Daoud Siniora.\n LOCATION:https://researchseminars.org/talk/OLS/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Sanders (Ruhr-Universität Bochum) DTSTART:20230831T180000Z DTEND:20230831T190000Z DTSTAMP:20260422T225801Z UID:OLS/140 DESCRIPTION:Title: Th e Biggest Five of Reverse Mathematics\nby Sam Sanders (Ruhr-Universit ät Bochum) as part of Online logic seminar\n\n\nAbstract\nI provide an ov erview of joint work with Dag Normann on the higher-order Reverse Mathemat ics (RM for short) of the Big Five systems and the surprising limits of th is enterprise ([3]).\n\nThe well-known Big Five phenomenon of RM is the ob servation that a large number of theorems from ordinary mathematics are ei ther provable in the base theory or equivalent to one of only four systems \; these five systems together are called the ‘Big Five’ of RM. The ai m of this paper is to greatly extend the Big Five phenomenon\, working in Kohlenbach’s higher-order RM ([1]).\n\nIn particular\, we have establish ed numerous equivalences involving the second-order Big Five systems on on e hand\, and well-known third-order theorems from analysis about (possibly ) discontinuous functions on the other hand. We both study relatively tame notions\, like cadlag or Baire 1\, and potentially wild ones\, like quasi -continuity. We also show that slight generalisations and variations (invo lving e.g. the notions Baire 2 and cliquishness) of the aforementioned thi rd-order theorems fall far outside of the Big Five. In particular\, these slight generalisations and variations imply the principle NIN from [2]\, i .e. there is no injection from [0\, 1] to N. We discuss a possible explana tion for this phenomenon.\n\nREFERENCES.\n\n[1] Ulrich Kohlenbach\, Higher order reverse mathematics\, Reverse mathematics 2001\, Lect. Notes Log.\, vol. 21\, ASL\, 2005\, pp. 281–295.\n\n[2] Dag Normann and Sam Sanders\ , On the uncountability of R\, Journal of Symbolic Logic\, DOI: doi.org/ 1 0.1017/jsl.2022.27 (2022)\, pp. 43.\n\n[3] _________________________\, The Biggest Five of Reverse Mathematics\, Submitted\, arxiv: https://arxiv.or g/abs/2212.00489 (2023)\, pp. 39.\n LOCATION:https://researchseminars.org/talk/OLS/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Noah Schweber (Proof School) DTSTART:20231012T180000Z DTEND:20231012T190000Z DTSTAMP:20260422T225801Z UID:OLS/141 DESCRIPTION:Title: Lo gic(s) in the computable context\nby Noah Schweber (Proof School) as p art of Online logic seminar\n\n\nAbstract\nIn abstract model theory\, ``lo gic" is typically defined as something like ``An indexed family of isomorp hism-respecting partitions of the class of all structures" - or more preci sely\, an assignment of such partitions to signatures (usually we demand s ome other conditions too). But we do not always think isomorphism-invarian tly\; in particular\, when thinking about computable structures we typical ly ``carve up" the universe into equivalence classes with respect to compu table isomorphism.\n\nIn this talk I'll explore what there is to be said a bout ``abstract model theory in the computable universe." One logic we'll pay particular attention to is gotten by mixing classical computable infin itary logic with the notion of realizability coming from intuitionistic ar ithmetic. This is work in progress\, so this talk will have lots of questi ons as well as results. No prior knowledge of intuitionistic logic will be assumed.\n LOCATION:https://researchseminars.org/talk/OLS/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Icard (Stanford University) DTSTART:20240411T180000Z DTEND:20240411T190000Z DTSTAMP:20260422T225801Z UID:OLS/142 DESCRIPTION:Title: Ca usal Inference as a Logical Problem\nby Thomas Icard (Stanford Univers ity) as part of Online logic seminar\n\n\nAbstract\nThe aim of this talk w ill be to explain how problems of modern causal inference can be usefully and precisely understood as logical problems. Causal inquiry introduces no vel angles on traditional themes in logic (complexity\, definability\, axi omatization\, etc.)\, and in the other direction\, mathematical and comput ational logic offers tools for clarifying questions in the theory of causa l inference.\n LOCATION:https://researchseminars.org/talk/OLS/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Russell Miller (City University of New York) DTSTART:20240118T190000Z DTEND:20240118T200000Z DTSTAMP:20260422T225801Z UID:OLS/143 DESCRIPTION:Title: Co mputability and absolute Galois groups\nby Russell Miller (City Univer sity of New York) as part of Online logic seminar\n\n\nAbstract\nThe ab solute Galois group $\\operatorname{Gal}(F)$\nof a field $F$ is the Ga lois group of its algebraic closure $\\overline{F}$\nrelative to $F$\, con taining precisely those automorphisms of $\\overline{F}$\nthat fix $F$ its elf pointwise. Even for a field as simple as the rational\nnumbers $\\mat hbb{Q}$\, $\\operatorname{Gal}(\\mathbb Q)$ is a complicated\nobject. Ind eed (perhaps counterintuitively)\, $\\operatorname{Gal}(\\mathbb Q)$\nis a mong the thorniest of all absolute Galois groups normally studied.\n\nWhen $F$ is countable\, $\\operatorname{Gal}(F)$ usually has the cardinality\n of the continuum. However\, it can be presented as the set of all paths\n through an $F$-computable finite-branching tree\, built by a procedure\nun iform in $F$. We will first consider the basic properties of this tree\,\ nwhich depend in some part on $F$. Then we will address questions\nabout the subgroup consisting of the computable paths through\nthis tree\, along with other subgroups\nsimilarly defined by Turing ideals. One naturally asks to what\nextent these are elementary subgroups of $\\operatorname{Gal }(F)$\n(or at least elementarily equivalent to $\\operatorname{Gal}(F)$).\ nThis question is connected to the computability of Skolem functions\nfor $\\operatorname{Gal}(F)$\, and also to the arithmetic complexity of\ndefin able subsets of $\\operatorname{Gal}(F)$.\n\nSome of the results that will appear represent joint work with\nDebanjana Kundu.\n LOCATION:https://researchseminars.org/talk/OLS/143/ END:VEVENT BEGIN:VEVENT SUMMARY:David Gonzalez (University of California Berkeley) DTSTART:20240201T190000Z DTEND:20240201T200000Z DTSTAMP:20260422T225801Z UID:OLS/144 DESCRIPTION:Title: Ge nerically computable linear orderings\nby David Gonzalez (University o f California Berkeley) as part of Online logic seminar\n\n\nAbstract\nW. C alvert\, D\, Cenzer and V. Harizanov introduced notions of generic computa bility for structures that are stratified by the computable ordinals. In a recent collaboration with these authors we examined these notions in the context of linear orderings. Our main results contrast one another. We sho w that every linear ordering has a 1-generically computable copy. On the o ther hand\, we have that the set of linear orderings with a n-generically computable copy for n>1 is as complicated as possible: Sigma 1 1-complete. \n\nThis talk will put these results in context and describe the new\, mor e structural approach we took to this problem. In particular\, I will desc ribe these results through the lens of a surprising connection with Ramsey -like properties.\n LOCATION:https://researchseminars.org/talk/OLS/144/ END:VEVENT BEGIN:VEVENT SUMMARY:David Meretzky (University of Notre Dame) DTSTART:20240509T180000Z DTEND:20240509T190000Z DTSTAMP:20260422T225801Z UID:OLS/145 DESCRIPTION:Title: Di fferential Field Arithmetic\nby David Meretzky (University of Notre Da me) as part of Online logic seminar\n\n\nAbstract\nI will discuss some of my upcoming thesis work under the supervision of Anand Pillay. Some of thi s work is also joint with Omar León Sánchez. Motivated by existence ques tions in differential Galois theory\, I will discuss our recent efforts to generalize a theorem of Serre from the algebraic to the differential alge braic setting. Serre's theorem states: A field F is bounded (has finitely many extensions of each finite degree) if and only if the first Galois coh omology set with coefficients in any linear algebraic group defined over F is trivial. This talk will emphasize our development of basic computatio nal tools for definable Galois cohomology\, a model theoretic generalizati on of (differential) algebraic Galois cohomology. All of the relevant noti ons will be introduced\, including some background on differential Galois theory.\n LOCATION:https://researchseminars.org/talk/OLS/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Ellen Hammatt (Victoria University of Wellington) DTSTART:20240215T190000Z DTEND:20240215T200000Z DTSTAMP:20260422T225801Z UID:OLS/146 DESCRIPTION:Title: Pu nctual Structures\nby Ellen Hammatt (Victoria University of Wellington ) as part of Online logic seminar\n\n\nAbstract\nIn this talk we investiga te what happens when we take concepts from computable structure theory and forbid the use of unbounded search. In other words\, we discuss the primi tive recursive content of structure theory. This central definition is tha t of punctual structures\, introduced by Kalimullin\, Melnikov and Ng in 2 017. We investigate various concepts from computable structure theory in t he primitive recursive case. A common theme is that new techniques are req uired in the primitive recursive case. We also discuss a degree structure within punctual presentations which is induced by primitive recursive isom orphisms. This degree structure is a new concept that does not arise in co mputable structure theory.\n LOCATION:https://researchseminars.org/talk/OLS/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamshid Derakhshan (Oxford University) DTSTART:20240208T190000Z DTEND:20240208T200000Z DTSTAMP:20260422T225801Z UID:OLS/147 DESCRIPTION:Title: De cidability of the class of all the rings $Z/mZ$: A problem of Ax\nby J amshid Derakhshan (Oxford University) as part of Online logic seminar\n\n\ nAbstract\nIn his celebrated 1968 paper on the elementary theory of finite fields James Ax asked if the theory of the class of all the rings $Z/mZ$\ , for all $m>1$\, is decidable. In that paper\, Ax proved that the existen tial theory of this class is decidable using his result that the theory of all the rings $Z/p^nZ$ (with $p$ and $n$ varying) is decidable. This used Chebotarev’s density theorem and Ax's pioneering work and axiomatizatio n of the theory of pseudo-finite fields. In that paper Ax proved that the theory of the class of all finite fields is decidable.\n\nIn this talk I w ill present joint work with Angus Macintyre giving a solution to Ax’s pr oblem. Our solution uses some previous work of ours on the model theory of the ring of adeles. These are locally compact rings associated to number fields and have been of fundamental importance in number theory ever since they were introduced by Chevalley\, Weil\, Artin. Interestingly Ax’s pr oblem can be reduced to the decidability of the ring of adeles of the rati onal numbers. So while the theory of pseudo-finite fields governs the theo ry of all finite fields as shown by Ax\, the theory of all $Z/mZ$ is gover ned by the theory of the rational adele ring.\n\n(This work is published i n Forum of Mathematics\, Sigma\, 24 July 2023.)\n LOCATION:https://researchseminars.org/talk/OLS/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Guingona (Towson University) DTSTART:20240314T180000Z DTEND:20240314T190000Z DTSTAMP:20260422T225801Z UID:OLS/148 DESCRIPTION:Title: Co nfigurations and Products of Classes\nby Vincent Guingona (Towson Univ ersity) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, I wi ll discuss the notion of a "configuration" where the index is a class of s tructures and the target is an arbitrary theory. This gives us a method o f classifying theories based on their ability to encode positive combinato rial configurations\, similar to the non-collapse of generalized indiscern ibles. We will examine desirable properties of the index class\, such as indivisibility\, and how these properties are closed under different produ ct operations.\n\nSome of this work is joint with M. Parnes and L. Scow.\n LOCATION:https://researchseminars.org/talk/OLS/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Miriam Parnes (Towson University) DTSTART:20240328T180000Z DTEND:20240328T190000Z DTSTAMP:20260422T225801Z UID:OLS/149 DESCRIPTION:by Miriam Parnes (Towson University) as part of Online logic s eminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/OLS/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Jessica Schirle (University of California Irvine) DTSTART:20240307T190000Z DTEND:20240307T200000Z DTSTAMP:20260422T225801Z UID:OLS/150 DESCRIPTION:Title: Ga ming Models by Buildings\nby Jessica Schirle (University of California Irvine) as part of Online logic seminar\n\n\nAbstract\nIn continuous mode l theory\, as in the classical setting\, if one has an appropriately sized unstable structure A in a countable language\, then depending on the trut h of CH\, there's either a unique or 2c many nonisomorphic ultr apowers of A as we vary the choice of ultrafilter on ω. A similar stateme nt may be made in regards to ultraproducts and sequences of structures tha t exhibit an order property.\n\nIn a partial answer to a question of Gromo v\, Kramer et al. showed that there is a finitely presented group such tha t\, depending on the truth of CH\, this group has either a unique or 2c many asymptotic cones up to homeomorphism. Asymptotic cones of me tric spaces are realized as particular metric ultraproducts. The Kramer et al. paper does not formalize the obvious model theoretic connection\, but does comment on the combinatorial-geometric structure of the asymptotic c ones\, which was known to Thornton (and independently to Kramer and Tent) and is a certain kind of building.\n\nIn this talk\, we'll give a brief ov erview of work done by Luther to formalize this model theoretic connection . Special attention will be given to Ehrenfeucht-Fraïssé games and how t he building structure can give us additional tools to develop a possible w inning strategy for Player II in games between (what are potentially) non- homeomorphic asymptotic cones of certain symmetric spaces.\n LOCATION:https://researchseminars.org/talk/OLS/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Coregliano (University of Chicago) DTSTART:20240926T180000Z DTEND:20240926T190000Z DTSTAMP:20260422T225801Z UID:OLS/152 DESCRIPTION:Title: Ex changeable random structures and quasirandomness\nby Leonardo Coreglia no (University of Chicago) as part of Online logic seminar\n\n\nAbstract\n A random structure on a vertex set $V$ (in a fixed finite relational langu age) is exchangeable if\nits distribution is invariant under permutations of $V$. The Aldous--Hoover Theorem says all such\ndistributions are genera ted from a collection of i.i.d. variables on $[0\,1]$\, one for each subse t\nof $V$\, using a simple rule that was later called "Euclidean structure " by combinatorialists. As the\nname suggests\, an Euclidean structure res embles a relational structure over $[0\,1]$\, except for the\npresence of "higher-order variables".\n\nOne of the original questions of Hoover was t o determine which such distributions admit simpler\ndescriptions\, that do not depend on certain variables. Very little progress was obtained in thi s\nproblem until it got revisited under the light of the theories of limit s of combinatorial objects\nand quasirandomness. It turns out that asking for a representation of an exchangeable hypergraph in\nwhich the Euclidean structure is a usual (measurable) relational structure over $[0\,1]$ (i.e .\, which\ndoes not need any higher-order variables) is equivalent to aski ng for "tamer" Szemeré\;di regularity\nlemmas and was solved using t he theory of hypergraphons.\n\nThe dual problem of determining when there is a representation that does not need any low-order\nvariable is more clo sely related to quasirandomness\, which informally is the property of "lac k of\ncorrelation with simple structures".\n\nIn this talk\, I will introd uce exchangeability and quasirandomness theory and talk about recent\nprog ress on the aforementioned dual problem. I will assume familiarity with ba sic logic/model\ntheory\, but no prior knowledge in extremal combinatorics \, limit theory or quasirandomness will be\nnecessary.\n\nThis talk is bas ed on joint works with Alexander Razborov and Henry Towsner.\n LOCATION:https://researchseminars.org/talk/OLS/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Zilli (Iowa State University) DTSTART:20240425T180000Z DTEND:20240425T190000Z DTSTAMP:20260422T225801Z UID:OLS/153 DESCRIPTION:Title: On the spectra of computable bounded analytic functions\nby Brian Zilli (Iowa State University) as part of Online logic seminar\n\n\nAbstract\nMcN icholl\, in collaboration with Matheson and later individually\, showed th at a Blaschke product is computable if and only if it has a computable zer o sequence with computable Blaschke constant. The spectrum of a Blaschke p roduct is the set of accumulation points of its zeros. We use Matheson and McNicholl's results to consider the arithmetical complexity of such spect ra for computable Blaschke products. Namely\, we present results showing t hat all such spectra are $\\Sigma^0_3$--closed\, that there exists a $\\Si gma^0_3$--complete spectrum\, that every $\\Pi^0_2$--closed subset of the unit circle is a spectrum\, and that there exists a $\\Sigma^0_2$--closed set which is not.\n\n\nWe then turn our attention to uniform Frostman Blas chke products\, shown by Frostman to be those with nontangential limits of modulus one everywhere (as opposed to generic Blaschke products which\, a s inner functions\, are only guaranteed to have radial limits of modulus o ne almost everywhere). Matheson showed that the spectra of such functions are precisely the closed\, nonempty\, and nowhere dense subsets of the uni t circle. We discuss an effectivization of one direction of his result\, s howing that every computably closed\, nonempty\, and nowhere dense subset of the circle is the spectrum of a computable uniform Frostman Blaschke pr oduct.\n\nJoint work with Timothy McNicholl\n LOCATION:https://researchseminars.org/talk/OLS/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo E. Coniglio (University of Campinas (UNICAMP)) DTSTART:20240502T180000Z DTEND:20240502T190000Z DTSTAMP:20260422T225801Z UID:OLS/154 DESCRIPTION:Title: De cision procedures for Intuitionistic logic and for modal logic S4 by 3-val ued non-deterministic matrices\nby Marcelo E. Coniglio (University of Campinas (UNICAMP)) as part of Online logic seminar\n\n\nAbstract\nIn 1932 Gödel proved that it is impossible to characterize\nintuitionistic propo sitional logic (IPL) by a single finite logical\nmatrix\, that is\, by fin ite-valued truth-tables. By adapting Gödel's\nproof\, J. Dugundji proved in 1940 that no modal system between Lewis'\nS1 and S5 can be characterize d by a single finite logical matrix. That\nis\, the usual modal logics are also not characterizable by finite-valued\ntruth-tables. As a way to over come Dugundji’s result\, J. Kearns\nintroduced in 1981 a 4-valued non-de terministic matrix (Nmatrix\, for\nshort) for modal logics KT\, S4\, and S 5 in which just a subset of the\nvaluations are allowed (that valuations a re called "level\nvaluations"). He proved that this restricted Nmatrix (RN matrix\, for\nshort) constitutes a sound and complete semantics for these modal\nlogics. However\, Kearns’s level valuations fail to provide an\ne ffective decision procedure for these modal logics. Recently\, L.\nGrätz refined Kearn’s original RNmatrix to obtain a decidable 3-valued\nRNmatr ix for modal logics KT and S4\, by using an appropriate\nnotion of partial valuation for level semantics.\nThanks to the conservative translation fr om IPL into S4 introduced by\nGödel in 1933\n(which is also computable)\, by composing both algorithms a decision\nprocedure for IPL is obtained.\n \nIn this talk the Grätz algorithm will be described\, as well as a new a lgorithm\nfor deciding validity in IPL obtained by considering another tra nslation\nderived from Gödel's one. It allows defining the composed algor ithm\nfor IPL above mentioned\, but in a direct way\, hence the soundness and\ncompleteness of the method is proved independently of Gödel and Grä tz results.\nIn this way\, an original 3-valued RNmatrix for IPL is define d\, with a\nvery natural\ninterpretation\, as well as an easy algorithm wh ich allows to remove\,\nfrom the truth\ntables generated by the 3-valued N matrix\, those rows which are not\nsound. This decision\nprocedure\, as we ll as Grätz's one\, were implemented in Coq. This is a\njoint work with R enato\nLeme and Bruno Lopes.\n LOCATION:https://researchseminars.org/talk/OLS/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Java Darleen Villano (University of Connecticut) DTSTART:20241024T180000Z DTEND:20241024T190000Z DTSTAMP:20260422T225801Z UID:OLS/155 DESCRIPTION:Title: Co mputable categoricity relative to a degree\nby Java Darleen Villano (U niversity of Connecticut) as part of Online logic seminar\n\n\nAbstract\nA computable structure $\\mathcal{A}$ is said to be computably categorical relative to a degree $\\mathbf{d}$ if for all $\\mathbf{d}$-computable cop ies $\\mathcal{B}$ of $\\mathcal{A}$\, there exists a $\\mathbf{d}$-comput able isomorphism between $\\mathcal{A}$ and $\\mathcal{B}$. In 2021 result by Downey\, Harrison-Trainor\, and Melnikov\, it was shown that there exi sts a computable graph $\\mathcal{G}$ such that for an infinite increasing sequence of c.e.\\ degrees $\\mathbf{x}_0 <_T \\mathbf{y}_0 <_T \\mathbf{ x}_1 <_T \\mathbf{y}_1\\dots$\, $\\mathcal{G}$ was computably categorical relative to each $\\mathbf{x}_i$ but not computably categorical relative t o each $\\mathbf{y}_i$.  That is\, the behavior of categoricity relative to a degree is not monotonic under $\\mathbf{0}'$. In this talk\, we will sketch how to extend this result for partial orders of c.e.\\ degrees\, an d discuss some future directions of this project.\n LOCATION:https://researchseminars.org/talk/OLS/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Jinhe Ye (University of Oxford) DTSTART:20241010T180000Z DTEND:20241010T190000Z DTSTAMP:20260422T225801Z UID:OLS/156 DESCRIPTION:Title: Hy perbolicity and model complete fields\nby Jinhe Ye (University of Oxfo rd) as part of Online logic seminar\n\n\nAbstract\nGiven $C$ a (quasi-proj ective) curve over $\\mathbb{Q}$ with genus at least 2 and $C(\\mathbb{Q}) $ is empty\, the class of fields $K$ of characteristic 0 such that $C(K)=\ \emptyset$ has a model companion CXF. Models of CXF have an interesting co mbination of properties and provide examples to answer various questions a round model theory of fields\, field arithmetic\, and decidability.\n\nIt turns out the existence of model companion is related to several notions o f hyperbolicity in algebraic geometry. In particular\, with the assumption s of different notions of hyperbolicity on V\, our results admit generalis ation to varieties V of arbitrary dimension. This talk is based on joint w ork with Will Johnson and joint work with Michal Szachniewicz.\n LOCATION:https://researchseminars.org/talk/OLS/156/ END:VEVENT BEGIN:VEVENT SUMMARY:Leo Jimenez (Ohio State University) DTSTART:20240912T180000Z DTEND:20240912T190000Z DTSTAMP:20260422T225801Z UID:OLS/157 DESCRIPTION:Title: In ternality of autonomous systems of differential equations\nby Leo Jime nez (Ohio State University) as part of Online logic seminar\n\n\nAbstract\ nWhen solving a differential equation\, one sometimes finds that solutions can be expressed using a finite number of fixed\, particular solutions\, and some complex numbers. As an example\, the set of solutions of a linear differential equation is a finite-dimensional complex vector space. A mod el-theoretic incarnation of this phenomenon is internality to the constant s in a differentially closed field of characteristic zero. In this talk\, I will define what this means\, and discuss some recent progress\, joint w ith Christine Eagles\, on finding concrete methods to determine whether or not the solution set of a differential equation is internal. A corollary of our method also gives a criteria for solutions to be Liouvillian: I wil l show a concrete application to Lotka-Volterra systems.\n LOCATION:https://researchseminars.org/talk/OLS/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Julia Knight (Notre Dame) DTSTART:20241121T190000Z DTEND:20241121T200000Z DTSTAMP:20260422T225801Z UID:OLS/158 DESCRIPTION:Title: Co mplexity of well-ordered sets in an ordered Abelian group\nby Julia Kn ight (Notre Dame) as part of Online logic seminar\n\n\nAbstract\nWe consid er the following three basic problems\, plus some variants.\n\n1. How hard is it to say of a countable well-ordering that it has type at least $\\al pha$?\n\n2. How hard is it to say of well-ordered sets $A\,B$ in an ordere d Abelian group $G$ that the set $A+B = \\{a+b:a\\in A\\ \\&\\ b\\in B\\}$ has type at least $\\alpha$?\n\n3. How hard is it to say of a well-ordere d set $A$ of non-negative elements in an ordered Abelian group $G$ that th e set $[A]$ consisting of finite sums of elements of $A$ has type at least $\\alpha$? \n\n\nEach problem asks the complexity of membership a smaller class $K$\, assuming membership in a larger class $K^*$. We want to meas ure complexity in the Borel and effective Borel hierarchies. However\, th e classes $K^*$ and $K$ are not Borel. Calvert's notions of complexity an d completeness within allow us to measure complexity in the way we want\, setting upper bounds\, and showing that the bounds are sharp. \n\n Authors: Chris Hall\, Julia Knight\, and Karen Lange\n LOCATION:https://researchseminars.org/talk/OLS/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles McCoy (University of Portland) DTSTART:20241107T190000Z DTEND:20241107T200000Z DTSTAMP:20260422T225801Z UID:OLS/159 DESCRIPTION:Title: Co mputable $\\Pi^0_2$ Scott Sentences\nby Charles McCoy (University of P ortland) as part of Online logic seminar\n\n\nAbstract\nAbstract available at http://lagrange.math.siu.edu/Calvert/OnlineSeminar/McCoy2024abstract.p df\n LOCATION:https://researchseminars.org/talk/OLS/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Dicle Mutlu (McMaster University) DTSTART:20241114T190000Z DTEND:20241114T200000Z DTSTAMP:20260422T225801Z UID:OLS/160 DESCRIPTION:Title: De finable groups in henselian valued fields\nby Dicle Mutlu (McMaster Un iversity) as part of Online logic seminar\n\n\nAbstract\nA valued field is henselian if every simple root of a polynomial in its residue field lifts uniquely to a root in the field itself. The Ax-Kochen-Ershov Principle st ates that henselian valued fields are—in the model-theoretic sense—det ermined by their value groups and residue fields\, which are much simpler mathematical structures. This naturally leads to the question: Can every d efinable group in a henselian valued field be decomposed into components t hat are controlled by its value group and residue field? Hrushovski and Ri deau-Kikuchi have answered this question positively for abelian groups in algebraically closed valued fields. In this talk\, we will discuss our app roach and results extending their work to the broader henselian setting. T his is joint work with Paul Z. Wang.\n LOCATION:https://researchseminars.org/talk/OLS/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Sunil Karn (Southern Illinois University) DTSTART:20241205T190000Z DTEND:20241205T200000Z DTSTAMP:20260422T225801Z UID:OLS/161 DESCRIPTION:Title: Be haviorally Correct Language Identification.\nby Sunil Karn (Southern I llinois University) as part of Online logic seminar\n\n\nAbstract\nThe con cept of Behaviorally Correct (BC) language identification\, is a paradigm in inductive inference that allows learners to approximate target language s while tolerating a bounded density of errors. Beginning with foundationa l definitions\, such as those of inductive inference machines (IIMs) and B C identification\, we extend these notions to approximate identification u sing error densities and asymptotic uniform densities. Our results demonst rate the structured inclusion relations between various identification cla sses. Specifically\, we prove that for any r\, r1​∈ [0\,1] with r1​> r\, TxtBCr ​⊂ TxtBCr1\, and similarly UBCr​ ⊂ UBCr1​​ and UTx tBCr ​⊂ UTxtBCr1\, indicating that relaxation of error bounds yields s trictly larger identification classes.\n\nFurthermore\, leveraging the Ope rator Recursion Theorem\, we construct examples demonstrating the non-equi valence of adjacent identification classes\, highlighting the role of part ial recursive functions in these separations. These results emphasize the versatility of BC identification frameworks in accommodating error densiti es while maintaining robust theoretical guarantees. Finally\, we introduce uniform approximate BC identification and establish its utility in addres sing local inconsistencies within language approximation\, culminating in refined criteria that bridge global and local error bounds.\n LOCATION:https://researchseminars.org/talk/OLS/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Don Stull (University of Chicago) DTSTART:20241003T180000Z DTEND:20241003T190000Z DTSTAMP:20260422T225801Z UID:OLS/162 DESCRIPTION:Title: Re cent progress on distance sets in the plane\nby Don Stull (University of Chicago) as part of Online logic seminar\n\n\nAbstract\nRecent work has shown that techniques from algorithmic randomness can be used to understa nd questions in classical geometric measure theory. One of the central pro blems in geometric measure theory is Falconer's distance set conjecture. G ive a set E in the plane\, and a point x\, the pinned distance set of E wi th respect to x is the set of distances between x and the points in E. In this talk\, I will discuss recent work which uses algorithmic randomness t o improve the best known lower bounds for both the Hausdorff and packing d imensions of pinned distance sets. This is joint work with Jacob Fiedler.\ n LOCATION:https://researchseminars.org/talk/OLS/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Janani Lakshmanan (University of Hawaii) DTSTART:20241031T180000Z DTEND:20241031T190000Z DTSTAMP:20260422T225801Z UID:OLS/163 DESCRIPTION:Title: Ne w Measures of Automatic Complexity Arising from Quantum Logic\nby Jana ni Lakshmanan (University of Hawaii) as part of Online logic seminar\n\n\n Abstract\nThe automatic complexity of finite words was introduced by Shall it and Wang (2001). It measures the complexity of a word $x$ as the minimu m number of states of a finite automaton that uniquely accepts $x$. Here\, an automaton $M$ uniquely accepts a word $x$ if $x$ is the only word of l ength $|x|$ accepted by $M$. Via the digraph representation of automata we can view the computation of this number of states as a problem of extrema l graph theory. A quantum version of automatic complexity was first studie d by Kjos-Hanssen (2017). In this talk\, we explore several new measures o f automatic complexity motivated by the geometric subspace structure of th e automata and the associated quantum logic. In keeping with the Hallowe'e n spirit\, We consider some generalizations of quantum finite automata wit h the application of an immortality constraint\, considering a family of a utomata without dead states.\n LOCATION:https://researchseminars.org/talk/OLS/163/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Sanders (RUB Bochum) DTSTART:20241017T180000Z DTEND:20241017T190000Z DTSTAMP:20260422T225801Z UID:OLS/164 DESCRIPTION:Title: So me results in reverse mathematics inspired by proof mining\nby Sam San ders (RUB Bochum) as part of Online logic seminar\n\n\nAbstract\nThe study of (compact) metric spaces in second-order Reverse Mathematics (RM hereaf ter) is fundamentally based on separability conditions\, while the latter are generally avoided in proof mining to enable the extraction of good com putational data. Inspired by this observation\, we study basic properties of ‘unrepresented’ compact metric spaces in Kohlenbach’s higher-orde r RM\, i.e. we do not assume separability conditions. Our results are four -fold as follows\, each building on the next.\n\nMost definitions of compa ctness yield third-order theorems not provable from second-order comprehen sion axioms. Only one very specific choice of compactness definitions yiel ds equivalences involving the so-called Big Five of second-order RM.\n\nMa ny basic properties of compact metric spaces inhabit the range of hyperari thmetical analysis. Until recently\, few natural examples of the latter we re known.\n\nSome basic properties of compact metric spaces\, like the int ermediate value theorem\, are equivalent to countable choice as studied in higher-order RM\, namely QF-AC0\,1.\n\nSome basic properties of compact m etric spaces\, like a continuous function has a supremum and a countable s et has measure zero\, imply strong axioms including Feferman’s projectio n principle\, full second-order arithmetic\, and Kleene’s quantifier ( ∃3).\n\nIn conclusion\, the removal of separability conditions from comp act metric spaces results in rather interesting phenomena.\n LOCATION:https://researchseminars.org/talk/OLS/164/ END:VEVENT BEGIN:VEVENT SUMMARY:Victoria Gitman (CUNY Graduate Center) DTSTART:20250206T190000Z DTEND:20250206T200000Z DTSTAMP:20260422T225801Z UID:OLS/165 DESCRIPTION:Title: Pa rameter-free schemes in second-order arithmetic\nby Victoria Gitman (C UNY Graduate Center) as part of Online logic seminar\n\n\nAbstract\nSecond -order arithmetic has two types of objects: numbers and set of numbers\, w hich we think of as the reals. Which sets (reals) have to exist in a model of second-order arithmetic is determined by the various set-existence axi oms. These usually come in the form of schemes\, of which the most common are the comprehension scheme\, the choice scheme\, and the collection sche me. The \\emph{comprehension scheme} $\\Sigma^1_n$-${\\rm CA}$ asserts for a $\\Sigma^1_n$-formula $\\varphi(n\,A)$\, with a set parameter $A$\, tha t the collection it determines is a set. The \\emph{choice scheme} $\\Sigm a^1_n$-${\\rm AC}$ asserts for a $\\Sigma^1_n$-formula $\\varphi(n\,X\,A)$ that if for every number $n$ there is a set $X$ such that $\\varphi(n\,X\ ,A)$ holds\, then there is a single set $Y$ such that its slice $Y_n$ is a witness for $n$. The \\emph{collection scheme} $\\Sigma^1_n$-${\\rm Coll} $ asserts more generally that among the slices of $Y$\, there is a witnes s for every $n$. The full comprehension scheme for all second-order assert ions is denoted by ${\\rm Z}_2$\, the full choice scheme by ${\\rm AC}$\, and the full collection scheme by ${\\rm Coll}$. Although the theories ${\ \rm Z}_2$+${\\rm AC}$ and ${\\rm Z}_2$ are equiconsistent\, Feferman and L \\' evy showed that ${\\rm AC}$ is independent of ${\\rm Z}_2$. It is also not difficult to see that ${\\rm Coll}$ implies ${\\rm Z}_2$ over $\\Sigm a^1_0$-${\\rm CA}$\, and hence that ${\\rm Coll}$ implies ${\\rm AC}$ over $\\Sigma^1_0$-${\\rm CA}$.\n\nIn this talk\, I will explore how significa nt the inclusion of set parameters is in the second-order set-existence sc hemes. Let ${\\rm Z}_2^{-p}$\, ${\\rm AC}^{-p}$\, and ${\\rm Coll}^{-p}$ d enote the respective parameter-free schemes. H. Friedman showed that the t heories ${\\rm Z}_2$ and ${\\rm Z}_2^{-p}$ are equiconsistent and recently Kanovei and Lyubetsky showed that the theory ${\\rm Z}_2^{-p}$ can have e xtremely badly behaved models in which the sets aren't even closed under c omplement. They also constructed a more ``nice" model of ${\\rm Z}_2^{-p}$ in which $\\Sigma^1_2$-${\\rm CA}$ holds\, but $\\Sigma^1_4$-${\\rm CA}$ fails. They asked whether one can construct a model of ${\\rm Z}_2^{-p}$ i n which $\\Sigma^1_2$-${\\rm CA}$ holds\, but there is an optimal failure of $\\Sigma^1_3$-${\\rm CA}$. I will answer their question by constructing such a model. I will also construct a model of ${\\rm Z}_2^{-p}+{\\rm Col l}^{-p}$ in which $\\Sigma^1_2$-${\\rm CA}$ holds\, but ${\\rm AC}^{-p}$ f ails\, thus showing that ${\\rm Coll}^{-p}$ does not imply ${\\rm AC}^{-p} $ even over $\\Sigma^1_2$-${\\rm CA}$.\n LOCATION:https://researchseminars.org/talk/OLS/165/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolaos Galatos (University of Denver) DTSTART:20250403T180000Z DTEND:20250403T190000Z DTSTAMP:20260422T225801Z UID:OLS/166 DESCRIPTION:Title: Ti ght complexity bounds for substructural logics\nby Nikolaos Galatos (U niversity of Denver) as part of Online logic seminar\n\n\nAbstract\nSubstr uctural logics constitute generalizations of classical and intuitionistic logic that allow for resource sensitive reasoning\; they connect to philos ophy\, computer science\, engineering\, mathematical linguistics and theor etical physics. Their algebraic semantics\, residuated lattices\, have the ir independent history and relate to ring theory\, lattice-ordered groups and Tarski’s relation algebras\, among other algebraic structures. \n\n We discuss the complexity of provability and of deduciblity of various sub structural logics\, ranging from low complexity classes to undecidability. Of particular interest are certain knotted extensions which have (non-ele mentary) complexity in the Ackermann level of the fast-growing hierarchy. We obtain lower complexity bounds by encoding suitable and-branching count er machines into the corresponding algebraic semantics\, using the method of residuated frames. For the upper bounds\, we undertake a proof-theoreti c investigation of auxiliary analytic calculi and employ methods from the theory of well-ordered sets to obtain length theorems. Together\, these yi eld tight complexity bounds for the logics under investigation. Our result s cover both sequent and hypersequent calculi.\n LOCATION:https://researchseminars.org/talk/OLS/166/ END:VEVENT BEGIN:VEVENT SUMMARY:Ulla Karhumäki (University of Helsinki) DTSTART:20250220T190000Z DTEND:20250220T200000Z DTSTAMP:20260422T225801Z UID:OLS/167 DESCRIPTION:Title: Ps eudofinite primitive permutation groups of finite SU-rank\nby Ulla Kar humäki (University of Helsinki) as part of Online logic seminar\n\n\nAbst ract\nA (definably) primitive permutation group (G\,X) is a group G togeth er with a transitive faithful and definable action on X such that there ar e no proper nontrivial (definable) G-invariant equivalence relations on X. Definably primitive permutation groups of finite Morley rank are well-stu died: in particular\, it is shown by Macpherson and Pillay that such a gro up with infinite point stabilisers is actually primitive and by Borovik an d Cherlin that\, given such a group (G\,X)\, the Morley rank of G can be b ounded in terms of the Morley rank of X. We show similar results for a pse udofinite definably primitive permutation group (G\,X) of finite SU-rank: we first show that (G\,X) is primitive if and only if the point stabiliser s are infinite. This then allows us to apply a classification result by Li ebeck\, Macpherson and Tent on (G\,X) so that we may bound the SU-rank of G in terms of the SU-rank of X. This is joint work in with Nick Ramsey.\n LOCATION:https://researchseminars.org/talk/OLS/167/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew DeLapo (University of Connecticut) DTSTART:20250213T190000Z DTEND:20250213T200000Z DTSTAMP:20260422T225801Z UID:OLS/168 DESCRIPTION:Title: In dex Sets and Computable Categoricity of CSC Spaces\nby Andrew DeLapo ( University of Connecticut) as part of Online logic seminar\n\n\nAbstract\n Given a topology on the natural numbers\, how complicated is it to describ e? To answer this question with tools from computability theory\, we will restrict to the context of countable second-countable (CSC) topological sp aces. One approach is to assign an index to each computable CSC space and determine the arithmetic complexity of the set of CSC spaces with some pro perty. Another approach comes from computable structure theory\; for examp le\, given two computable copies of a CSC space\, does there exist a compu table homeomorphism between them? In this talk\, we will explore these app roaches and apply them in three running examples: the indiscrete\, discret e\, and initial segment topologies.\n LOCATION:https://researchseminars.org/talk/OLS/168/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodore Slaman (University of California Berkeley) DTSTART:20250123T190000Z DTEND:20250123T200000Z DTSTAMP:20260422T225801Z UID:OLS/169 DESCRIPTION:Title: Ex tending Borel's Conjecture from Measure to Dimension\nby Theodore Slam an (University of California Berkeley) as part of Online logic seminar\n\n \nAbstract\nWe discuss the general formulation of Hausdorff dimension in t erms of gauge measures from the meta-mathematical perspective. There is a natural generalization to the context of dimension of Borel's conjecture that only countable sets have strong measure zero. We show that this gene ralization is consistent with ZFC. \n\nWe propose the question "For which ideals I of gauge measures H does there exist a set such that H(A)>0 exac tly when H is an element of I?" We settle a question of C. Rogers (1962) to show that the answer to this question depends on the descriptive comple xity of A. In particular\, the answer for closed sets is different from t hat for (even low-level) Borel sets.\n LOCATION:https://researchseminars.org/talk/OLS/169/ END:VEVENT BEGIN:VEVENT SUMMARY:Pablo Barcelo (Pontificia Universidad Cató\;lica de Chile) DTSTART:20250320T180000Z DTEND:20250320T190000Z DTSTAMP:20260422T225801Z UID:OLS/170 DESCRIPTION:Title: Th e Role of Logic in Advancing Machine Learning: Three Case Studies\nby Pablo Barcelo (Pontificia Universidad Cató\;lica de Chile) as part o f Online logic seminar\n\n\nAbstract\nIn this paper\, I present three case studies from my collaborative research that highlight the essential role of logic in enhancing our understanding of modern machine learning archite ctures. The first two examples focus on the expressive capabilities of two prominent architectures: Transformers\, which have revolutionized NLP app lications\, and Graph Neural Networks\, a leading approach for classifying graph-structured data. We employ temporal logic techniques to analyze the properties that Transformers can recognize\, and modal logics to examine the properties discernible by Graph Neural Networks. The third example add resses the pursuit of explainable AI\, demonstrating how first-order logic can be used to design languages that declare\, evaluate\, and compute exp lanations for decisions made by machine learning models.\n LOCATION:https://researchseminars.org/talk/OLS/170/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Zambrano (Universidad Nacional de Colombia at Bogotá\; ) DTSTART:20250327T180000Z DTEND:20250327T190000Z DTSTAMP:20260422T225801Z UID:OLS/171 DESCRIPTION:Title: Qu antale-Valued Model Theory and Set Theory\nby Pedro Zambrano (Universi dad Nacional de Colombia at Bogotá\;) as part of Online logic semina r\n\n\nAbstract\nIn this talk\, we will discuss a generalization of Contin uous Logic\, where the distances take values in suitable quantales. By ass uming suitable conditions (e.g.\, being\nco-divisibility -substractability -\, being a co-Girard and a V-domain)\, we provide a proof of a version of the Tarski-Vaught test and Łoś Theorem in our setting. Iovino proved th at there is no logic properly extending Continuous Logic satisfying both C ountable Tarski-Vaught chain Theorem and Compactness Theorem\, obtaining i n this way a new approach of Continuous Logic. This part is a joint work w ith David Reyes. Also\, we will talk about a generalization of Fitting’s work on Intuitionistic Kripke models of Set Theory using Ono’s and Komo ri’s Residuated Kripke models. Based on these models\, we provide a gene ralization of the von Neumann hierarchy in the context of Modal Residuated Logic (close to quantales) and prove a translation of formulas between it and a suited Heyting valued model. This part is a joint work with Jose R. Moncayo.\n LOCATION:https://researchseminars.org/talk/OLS/171/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Nakid Cordero (University of Wisconsin) DTSTART:20250410T180000Z DTEND:20250410T190000Z DTSTAMP:20260422T225801Z UID:OLS/172 DESCRIPTION:Title: Ma rtin's conjecture in the enumeration degrees\nby Antonio Nakid Cordero (University of Wisconsin) as part of Online logic seminar\n\n\nAbstract\n Martin's conjecture is a long open problem that seeks to prove the empiric al observation that "naturally occurring" Turing degrees are well-ordered. The conjecture posits that the only natural constructions of incomputable degrees arise from iterations of the Turing jump. Even though the full co njecture remains open\, several significant partial results have been obta ined both in the Turing degrees and by translating the conjecture to other degree structures.\n\n The study of the enumeration degrees has gained r elevance in recent years for their applications to effective mathematics a nd for their structural connections to the Turing degrees. In this settin g\, Martin's conjecture is relevant due to the existence of a definable co py of the Turing degrees inside the enumeration degrees and two natural op erations that extend the Turing jump: the enumeration jump and the skip. H owever\, the unique features of the enumeration degrees pose challenges to even formulating an analogue to Martin's conjecture.\n\n I will present a surprising positive result based on Bard's local approach to the uniform Martin's conjecture. From this\, we can prove part 1 of Martin's conjectu re for uniformly Turing-to-enumeration invariant functions. Additionally\, I discuss several counterexamples\, including an invariant function in th e enumeration degrees that fails to be uniformly invariant.\n LOCATION:https://researchseminars.org/talk/OLS/172/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Pablo de Rasis (Ohio State University) DTSTART:20250306T190000Z DTEND:20250306T200000Z DTSTAMP:20260422T225801Z UID:OLS/173 DESCRIPTION:Title: De finability problems regarding Campana points and Darmon points\nby Jua n Pablo de Rasis (Ohio State University) as part of Online logic seminar\n \n\nAbstract\nCampana points and Darmon points arise in algebraic geometry to generalize m-full integers and perfect m-th powers\, respectively\, to more arbitrary varieties. In this talk we will study the problem of defin ing these objects over number fields using first-order language\, and we w ill conclude by building on a result by Fritz\, Pasten\, and Pheidas which shows that the diophantineness of Campana points on complex rational func tions in one variable is incompatible with Kollar's conjecture\, an argume nt that can be easily adapted for Darmon points as well. This will motivat e further research on the analogous definability of these sets over C(z).\ n LOCATION:https://researchseminars.org/talk/OLS/173/ END:VEVENT BEGIN:VEVENT SUMMARY:Isis Gallardo (University of Denver) DTSTART:20250313T180000Z DTEND:20250313T190000Z DTSTAMP:20260422T225801Z UID:OLS/174 DESCRIPTION:Title: De cidability and generation of the variety of distributive $\\ell$-pregroups .\nby Isis Gallardo (University of Denver) as part of Online logic sem inar\n\n\nAbstract\nLattice-ordered pregroups ($\\ell$-pregroups) represen t a natural generalization of lattice ordered groups ($\\ell$-groups). It is well-established that every $\\ell$-group can be embedded into a symmet ric one\, as demonstrated by Cayley-Holland’s embedding theorem. Analogo usly\, a Cayley-Holland’s embedding theorem exists for distributive $\\e ll$-pregroups\, asserting that any distributive $\\ell$-pregroup can be em bedded into a functional one. In this work\, we enhance this result by est ablishing that any distributive $\\ell$-pregroup can be embedded into a fu nctional one over a chain that is locally isomorphic to $\\mathbb{Z}$. Uti lizing this\, we demonstrate that the variety of distributive $\\ell$-preg roups is generated by the (single) functional algebra over the integers. W e will later use this to prove the decidability of the variety.\n LOCATION:https://researchseminars.org/talk/OLS/174/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicola Gambino (University of Manchester) DTSTART:20250227T190000Z DTEND:20250227T200000Z DTSTAMP:20260422T225801Z UID:OLS/175 DESCRIPTION:Title: Mo noidal bicategories\, differential linear logic\, and analytic functors\nby Nicola Gambino (University of Manchester) as part of Online logic se minar\n\n\nAbstract\nDifferential linear logic\, introduced by Ehrhard and Regnier\, is an extension of linear logic with a differentiation operatio n. It is interesting both from a syntactic point of view\, since it leads to a new technique to study λ-calculus (via Taylor series expansion of λ -terms)\, and a semantical one\, as its models are categories in which mor phisms can be differentiated. The talk will present a new model of differe ntial linear logic\, based on Joyal’s analytic functors\, which are a fu nctorial counterpart of exponential power series. This model can be unders tood as a ‘categorified’ version of the relational model of Linear Log ic.\n LOCATION:https://researchseminars.org/talk/OLS/175/ END:VEVENT BEGIN:VEVENT SUMMARY:Uri Andrews (University of Wisconsin) DTSTART:20250417T180000Z DTEND:20250417T190000Z DTSTAMP:20260422T225801Z UID:OLS/176 DESCRIPTION:Title: Gr oup word problems revisited\nby Uri Andrews (University of Wisconsin) as part of Online logic seminar\n\n\nAbstract\nPre-dating computability th eory\, Max Dehn proposed to find algorithms to answer\, for a given group presentation\, word problem of the group: whether two given words in the generators are equal in the group. Novikov and Boone showed in the 50s tha t some simply presented groups can have undecidable word problem. In fact\ , every r.e. degree contains the word problem of a finitely presented grou p. From the perspective of the Turing degrees\, this gives a complete answ er to the question of the complexity of word problems of groups. The answe r is: Every possible complexity.\n\nI will present a different perspective on studying word problem complexity: We study the complexity of word prob lems as equivalence relations under computable reducibility. That is\, we say that an equivalence relation R reduces to an equivalence relation E if there is a computable function f so that xRy if and only if f(x) E f(y). In this structure\, we find a more subtle picture\, beginning with the fac t that not every degree is the degree of a the word problem of a group. So me surprising phenomena appear. Work joint with Turbo Ho and Luca San Maur o.\n LOCATION:https://researchseminars.org/talk/OLS/176/ END:VEVENT BEGIN:VEVENT SUMMARY:Heidi Benham (University of Connecticut) DTSTART:20250424T180000Z DTEND:20250424T190000Z DTSTAMP:20260422T225801Z UID:OLS/177 DESCRIPTION:Title: Pr oblem Reducibility of Weakened Ginsburg—Sands Theorem\nby Heidi Benh am (University of Connecticut) as part of Online logic seminar\n\n\nAbstra ct\nA recent paper by Benham\, DeLapo\, Dzhafarov\, Solomon\, and Villano entitled “Ginsburg—Sands theorem and computability theory” analyzes computability theoretical and reverse mathematical strength of a topologic al theorem by Ginsburg and Sands\, along with several weakened versions. T he original theorem states that every infinite topological space has an in finite subspace homeomorphic to one of the following on the natural number s: indiscrete\, initial segment\, final segment\, discrete\, or cofinite. In this original paper\, it is claimed that the theorem is a consequence o f Ramsey’s Theorem\, and though it has been shown by Benham\, DeLapo\, D zhafarov\, Solomon\, and Villano that the full theorem is equivalent over RCA_0 to ACA_0\, there is a weakened version that is equivalent over RCA_0 to CAC (Chain-antichain Principle)\, a consequence of Ramsey’s Theorem. One interesting feature of the proof of this equivalence is that\, not on ly an application CAC\, but also an application of ADS (Ascending/descendi ng Sequence Principle)\, which is a consequence of CAC\, is used. This ins pires the question of whether this weakened version of the Ginsburg—Sand s Theorem and CAC\, when viewed as problems\, are Weihrauch equivalent.\n\ nI will present some new progress that has been made on this question. Thi s progress involves developing several new combinatorial problems related to CAC and ADS\, one of which is Weihrauch equivalent to the weakened vers ion of the Ginsburg—Sands Theorem\, and showing a variety of Weihrauch a nd computable reducibilities between them.\n LOCATION:https://researchseminars.org/talk/OLS/177/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Gamboa Guzmá\;n (Iowa State University) DTSTART:20250501T180000Z DTEND:20250501T190000Z DTSTAMP:20260422T225801Z UID:OLS/178 DESCRIPTION:Title: Fo rmalizing Time: Temporal Logics and the Challenge of Visualizing MLTL\ nby Laura Gamboa Guzmá\;n (Iowa State University) as part of Online logic seminar\n\n\nAbstract\nTemporal logics are a family of modal logics that reason about timelines. They are usually obtained by expanding classi cal propositional logic with modal operators that can qualify the value of a proposition over time\, such as “p will always be true” or “q is true until p becomes true.” However\, different concepts of time are oft en captured by significant logical systems\, as these tend to encode the v arious characteristics that define them\, such as continuous vs. discrete time and linear vs. branching time. The use and development of these logic s have been increasing significantly over the last 50 years\, as researche rs and engineers in fields related to computer science have been using the m to verify safety-critical systems in a formal and precise manner. \n\nIn this talk\, I will introduce some of the better-known temporal logics tha t aim to formalize different concepts of time and briefly explain the diff erent properties that make them good candidates for use in different compu ter-based environments. After that\, I will focus on a logic I have been w orking on during my PhD known as Mission-time (Linear) Temporal Logic (MLT L)\, which is a logic that reasons about finite and discrete timelines (ca lled traces) where finite intervals bound the temporal operators. Although MLTL is only as expressive as classical propositional logic\, it has been capturing the attention of multiple research groups in recent years\, and its succinctness has shown to become a challenge for engineers easily whe n trying to validate the formulas they believe are capturing the desired b ehaviors. For that\, at the Laboratory for Temporal Logic at ISU\, we have been developing algorithms that allow us to take an MLTL formula and prod uce a visual representation for the traces that satisfy the formula.\n LOCATION:https://researchseminars.org/talk/OLS/178/ END:VEVENT BEGIN:VEVENT SUMMARY:Krzysztof Mierzewski (Carnegie Mellon University) DTSTART:20250508T180000Z DTEND:20250508T190000Z DTSTAMP:20260422T225801Z UID:OLS/179 DESCRIPTION:Title: Th e logics of kernels and closures\nby Krzysztof Mierzewski (Carnegie Me llon University) as part of Online logic seminar\n\n\nAbstract\nEach subse t D of a complete Boolean algebra generates both a closure operator and a kernel operator on the algebra\, respectively mapping each element to its lower approximation (the join of all D-elements below it) and its upper ap proximation (the meet of all D-elements above it). I will discuss the bimo dal logics of such approximation operators on Boolean algebras. By varying the constraints imposed on the generating set D\, we obtain a natural fam ily of modal logics. The resulting algebraic approximation semantics offer s a new perspective on several common modal systems: I will show how well- known modal logics can be recovered as logics of approximation for particu lar choices of constraints on the generating set\, and one can trace the e mergence of various modal laws to simple structural features of the genera ting set. The logic of approximation operators generated by arbitrary subs ets D is the subnormal logic EMNT4+EMNT4. I will give a simple criterion t hat characterizes the corresponding class of algebras: that is\, algebras with abstract closure and kernel operators that are representable as appro ximation operators. The complete logic of approximation operators generate d by a sublattice is the fusion S4+S4: the completeness result relies on a correspondence between sublattice-generated approximation operators and p airwise zero-dimensional bitopological spaces. When D is a complete sublat tice\, we obtain exactly the temporal logic S4t. When D is a subalgebra\, the two modalities collapse into one as they become each other’s duals\, and we obtain monomodal S5 (for complete subalgebras) and S4 (for subalge bras in general).\n LOCATION:https://researchseminars.org/talk/OLS/179/ END:VEVENT BEGIN:VEVENT SUMMARY:Emma Gruner (Penn State University) DTSTART:20250904T180000Z DTEND:20250904T190000Z DTSTAMP:20260422T225801Z UID:OLS/180 DESCRIPTION:Title: A Baire Category Approach to Besicovitch's Theorem\nby Emma Gruner (Penn State University) as part of Online logic seminar\n\n\nAbstract\nOne of t he fundamental results from geometric measure theory is Besicovitch's theo rem from 1952\, which states that any closed subset of Euclidean space hav ing infinite Hausdorff measure contains a compact subset with positive fin ite Hausdorff measure. However\, the computatibility theoretic and reverse mathematical complexity of this result have not been extensively studied. In this talk\, we will introduce a variant of the Baire Category Theorem\ , and show how we can reframe Besicovitch's original proof through that le ns. This approach not only confirms that the theorem is provable in $\\tex t{ACA}_0$\, but demonstrates how a witnessing subset can be computed from just one jump of the original set.\n LOCATION:https://researchseminars.org/talk/OLS/180/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Poesia (Harvard University) DTSTART:20251106T190000Z DTEND:20251106T200000Z DTSTAMP:20260422T225801Z UID:OLS/181 DESCRIPTION:Title: Le arning formal mathematical abstractions\nby Gabriel Poesia (Harvard Un iversity) as part of Online logic seminar\n\n\nAbstract\nMathematical abst ractions are devices that enable general representations of many concrete mathematical objects at once: they include definitions\, lemmas\, proof st rategies and algorithms. Typically\, computer agents applied in formal mat hematics are given a set of human-created abstractions (e.g.\, definitions \, tactics\, lemmas in Lean's mathematical library) and receive tasks that involve using and combining those (e.g.\, proving a given theorem). This talk will instead focus on our work on automatically learning the abstract ions themselves. We'll first describe our initial work on this line on lea rning problem-solving tactics for Khan Academy algebra problems in a simpl e dependently-typed theorem proving environment. Then\, we will use these principles to learn tactics in the Rocq (formerly Coq) theorem prover from existing corpora of human proofs. In both cases\, tactic learning is oper ationalized by a symbolic compression procedure\, a principle that has bee n fruitful in learning abstractions in the field of program synthesis. I'l l end by briefly describing ongoing work on a compression-based library le arning method for terms in Lean's type theory\, and highlight several appl ications of this tool. In particular\, compressing sets of theorem stateme nts yields new mathematical definitions that help compactly rewrite the st atements\, whereas compressing proof terms gives rise to lemmas that short en existing proofs.\n LOCATION:https://researchseminars.org/talk/OLS/181/ END:VEVENT BEGIN:VEVENT SUMMARY:Annalisa Conversano (Massey University) DTSTART:20250828T180000Z DTEND:20250828T190000Z DTSTAMP:20260422T225801Z UID:OLS/182 DESCRIPTION:Title: Gr oups and rings in o-minimal structures\nby Annalisa Conversano (Massey University) as part of Online logic seminar\n\n\nAbstract\nAfter a short introduction to o-minimality\, I will try to explain connections and inter actions between groups and rings that are definable in arbitrary o-minimal structures and familiar objects over the real field: Lie groups and assoc iative algebras. All definitions will be recalled\, and many examples will be used to illustrate the general theory.\n LOCATION:https://researchseminars.org/talk/OLS/182/ END:VEVENT BEGIN:VEVENT SUMMARY:John Goodrick (Universidad de los Andes) DTSTART:20250918T180000Z DTEND:20250918T190000Z DTSTAMP:20260422T225801Z UID:OLS/183 DESCRIPTION:Title: Ex pansions of ordered Abelian groups by unary predicates\nby John Goodri ck (Universidad de los Andes) as part of Online logic seminar\n\n\nAbstrac t\nI will talk about some recent results on model-theoretic tameness prope rties of expansions of ordered Abelian groups by unary predicates. In part icular\, I will discuss properties such as (strongly) NIP\, having finite dp-rank\, and dp-minimality and how these relate to topological and arithm etic properties of sets definable in the structure. Furthermore I will pre sent some ongoing work on quantifier elimination for expansions of regular ordered abelian groups by a predicate for a dense subgroup.\n LOCATION:https://researchseminars.org/talk/OLS/183/ END:VEVENT BEGIN:VEVENT SUMMARY:Jin Wei (University of Pennsylvania) DTSTART:20251009T180000Z DTEND:20251009T190000Z DTSTAMP:20260422T225801Z UID:OLS/184 DESCRIPTION:Title: A Gentzen-Style Proof System for First-Order Łukasiewicz Logic and Its Comp leteness\nby Jin Wei (University of Pennsylvania) as part of Online lo gic seminar\n\n\nAbstract\nContinuous model theory for metric structures i s grounded in first-order Łukasiewicz logic and thus inherits an Hilbert- style axiomatization. However\, the syntactic study with this proof system encounters difficulties\, mainly the failure of the deduction theorem due to issues with contraction. Gentzen-style proof systems for Łukasiewicz Logic have been developed to address these challenges\, with hypersequent calculi for propositional and first-order Łukasiewicz Logic introduced by Metcalfe\, Olivetti\, and Gabbay (2005) and Baaz and Metcalfe (2010). In this talk\, I will give a brief introduction to their work and present my own result establishing the first-order completeness. I will also discuss potential directions of research\, including syntax cut elimination and th e development of a constructive fragment of Łukasiewicz Logic\, with pote ntial applications to continuous logic.\n LOCATION:https://researchseminars.org/talk/OLS/184/ END:VEVENT BEGIN:VEVENT SUMMARY:Cé\;cilia Pradic (Swansea University) DTSTART:20251016T180000Z DTEND:20251016T190000Z DTSTAMP:20260422T225801Z UID:OLS/185 DESCRIPTION:Title: Ho w unconstructive is the Cantor-Bernstein theorem?\nby Cé\;cilia Pradic (Swansea University) as part of Online logic seminar\n\n\nAbstract\ nBased on joint work with Chad Brown [1] and [2].\nThe Cantor-Bernstein th eorem states that sizes of sets can be compared meaningfully using injecti ons: if A injects into B and vice-versa\, A and B are in bijection. This i s typically proven via an explicit construction that does not involve choi ce\, but the proof cannot be constructive. For instance\, [0\,1] and (0\,1 ) can be embedded into one another but are not homeomorphic\, meaning that Cantor-Bernstein is violated in a number of models of intuitionistic set theory. Faced with this state of affairs\, we can still ask: how bad it is ?\nFirst\, we are going to see how Cantor-Bernstein implies full excluded middle. We will then turn our attention to the Myhill isomorphism theorem\ , a constructive version of Cantor-Bernstein that states that\, for any tw o subsets A\, B ⊆ ℕ that are inter-reducible via injections\, there is a bijection ℕ → ℕ that preserves them. The theorem remains true cla ssically if ℕ is replaced by an arbitrary set X\, but this is not the ca se constructively. Bauer asked if there is a nice class of sets X for whic h it does hold constructively. After checking there is no hope for this cl ass of sets to be closed under basic operations like disjoint unions\, we will see that a version of this generalized Myhill isomorphism theorem hol ds for the conatural numbers ℕ∞ by adapting the usual back-and-forth c onstruction and assuming Markov's principle. However\, this does not exten d much: this fails for 2× ℕ∞\, ℕ + ℕ∞ as well as Cantor space. We are going to see why those failures are of different flavours\, and ske tch how to make this more precise by using oracle modalities.\n\n1. Pradic \, C. and Brown\, C. E. 2022. Cantor-Bernstein implies Excluded Middle. ar Xiv preprint arXiv:1904.09193.\n\n2. Pradic\, C. 2025. The Myhill isomorph ism theorem does not generalize much. arXiv preprint arXiv:2507.05028.\n LOCATION:https://researchseminars.org/talk/OLS/185/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Freund (Universitä\;t Wü\;rzburg) DTSTART:20250925T180000Z DTEND:20250925T190000Z DTSTAMP:20260422T225801Z UID:OLS/186 DESCRIPTION:Title: We ll-ordering principles and the reverse mathematics zoo\nby Anton Freun d (Universitä\;t Wü\;rzburg) as part of Online logic seminar\n\n\n Abstract\nOver the moderately strong base theory ACA$_0$ from reverse math ematics\, any $\\Pi^1_2$-statement corresponds to a transformations of wel l-orders (i.e.\, to a dilator). We will show that\, in contrast\, there is a dichotomy over the weaker base theory RCA$_0$. Here\, transformations o f well-orders are either weak or have a certain minimal strength. It follo ws that $\\Pi^1_2$-statements in a certain gap cannot correspond to a tran sformation of well-orders. Ramsey's theorem for pairs is a particularly pr ominent $\\Pi^1_2$-statement in this gap. The talk is based on https://doi.org/10.1142/S02190613 25500102. It is directed at a general logical audience.\n LOCATION:https://researchseminars.org/talk/OLS/186/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Block (College of William & Mary) DTSTART:20251113T190000Z DTEND:20251113T200000Z DTSTAMP:20260422T225801Z UID:OLS/187 DESCRIPTION:Title: Me asuring the Complexity of Countable Models of Presburger Arithmetic\nb y Jason Block (College of William & Mary) as part of Online logic seminar\ n\n\nAbstract\nWe examine two methods for classifying the complexity of co untable structures: degree spectra\, and Scott analysis. Degree spectra me asure how difficult it is to compute copies of structures\, while Scott an alysis measures the complexity of describing structures up to isomorphism. We examine the possible degree spectra and Scott complexities of countabl e Presburger groups and compare these results with those for models of Pea no Arithmetic. We also discuss how these measures of complexity succeed/fa il in distinguishing the intended model of the theory.\n LOCATION:https://researchseminars.org/talk/OLS/187/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Alm (Southern Illinois University) DTSTART:20251002T180000Z DTEND:20251002T190000Z DTSTAMP:20260422T225801Z UID:OLS/188 DESCRIPTION:Title: Re lation Algebra and Sumset Problems in Abelian Groups\nby Jeremy Alm (S outhern Illinois University) as part of Online logic seminar\n\n\nAbstract \nAn abstract relation algebra (RA) is called representable if it embeds i n a collection of binary relations closed under union\, complementation\, composition\, conversion\, and identity. The question of representability is undecidable for finite RAs. It is therefore of interest to impose vario us restrictions on the RAs or on the representations themselves in order t o narrow the search space. \n\nFor example\, one might consider only so-ca lled "cyclic" representations\, which affords a log-quadratic improvement in search time. If we further assume that the automorphism group of the al gebra A with c "colors" (symmetric diversity atoms) contains a cycle of le ngth c\, and consider only those cyclic representations that arise via a f inite field method (due to Comer)\, we actually get decidability: we can check for Comer representations of A in O(c^8 / log c) time. \n\nIf an RA A has no 3-cycles ("rainbow triangles")\, then representability of A is de cidable without restriction on the "type" of representation\, a result due to Maddux. \n\nA "Goldilocks" happy medium might be found by restricting attention to representations over abelian groups more generally. In this context\, problems can be stated in terms of sumset conditions for partiti ons of the group. For example\,\n\nFor which finite abelian G does there e xist a partition G = {0} u A u B such that\n\n\n\n\nThis formulation has two real advantages: fi rst\, the problem is understandable to any mathematician\; second\, we can bring in results from the additive number theory literature. \n\nNotice t hat the set B above is a sum-free set. Constructing sum-free sets with ot her desired properties is difficult in general. We will discuss this in th e context of a problem I've been working on for almost 20 years.\n LOCATION:https://researchseminars.org/talk/OLS/188/ END:VEVENT BEGIN:VEVENT SUMMARY:Yatir Halevi (Technion - Israel Institute of Technology) DTSTART:20251120T190000Z DTEND:20251120T200000Z DTSTAMP:20260422T225801Z UID:OLS/189 DESCRIPTION:Title: Ar ound Taylor’s Conjecture and Model-Theoretic Tameness\nby Yatir Hale vi (Technion - Israel Institute of Technology) as part of Online logic sem inar\n\n\nAbstract\nGiven a graph (G\, E)\, its chromatic number is the sm allest cardinal\n$\\kappa$ admitting a legal coloring of the vertices.\nTh e strong Taylor's conjecture states the following:\n\nIf G is an infinite graph with chromatic number $\\geq \\aleph_1$\, then\nit contains all fin ite subgraphs of $Sh_n(\\omega)$ for some n\,\nwhere $Sh_n(\\omega)$ is th e n-shift graph (which we will introduce).\n\nThe conjecture was disproved by Hajnal and Komjáth\; however\, a variant\nof it still holds for $\\om ega$-stable\, superstable\, or stable graphs.\nOne can also restrict the c onjecture and ask when G contains all\nfinite subgraphs of the complete gr aph.\nWe give answers to this question when the edge relation of the graph \nis stable or when the graph itself is simple.\n\nJoint work with Itay Ka plan and Saharon Shelah\n LOCATION:https://researchseminars.org/talk/OLS/189/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilda Ferreira (Universidade Aberta and CEMS UL) DTSTART:20260115T190000Z DTEND:20260115T200000Z DTSTAMP:20260422T225801Z UID:OLS/190 DESCRIPTION:Title: Fr om Commuting Conversions to Syntactic Identity\nby Gilda Ferreira (Uni versidade Aberta and CEMS UL) as part of Online logic seminar\n\n\nAbstrac t\nCommuting conversions are often regarded as the "price to pay'' for seq uential syntax in natural deduction proofs or even as a sign of ``syntacti c inadequacy''. This presentation explores translations of the Intuitionis tic Propositional Calculus (IPC) into systems with no commuting conversion s.\n\nAn example of such translations is the well-known Russell-Prawitz tr anslation which maps IPC into a highly expressive system known as System F \, or polymorphic lambda calculus. Despite the elegance of this embedding\ , it fails to preserve proof reduction or even proof identity.\n\nWe will explore two different strategies for achieving proof identity preservation . The first strategy involves replacing System F with an atomic polymorphi c target system. We will present and compare different versions of the Rus sell-Prawitz translation that follow this strategy [1\,2\,3]. The second s trategy consists of introducing new atomization conversions to System F [4 ]\, obtaining not only proof identity preservation but also reduction pres ervation.\n\nA recently developed translation [5]\, which completely avoid s commuting conversions\, shows that via the first strategy we can also ac hieve reduction preservation. Moreover\, this new translation maps commuti ng conversions to syntactic identity\, achieving a cleaner\, ``commuting-c onversion-free'' image of IPC.\n\nThis presentation includes significant j oint work with José Espírito Santo.\n\n1. F. Ferreira\, G. Ferreira\, At omic polymorphism\, The Journal of Symbolic Logic\, 78(1)\, pp. 260-274\, 2013.\n\n2. P. Pistone\, L. Tranchini\, M. Petrolo\, The naturality of nat ural deduction (II): On atomic polymorphism and generalized propositional connectives\, Studia Logica\, 110\, pp. 545-592\, 2022.\n\n3. J. Espírito Santo\, G. Ferreira\, A refined interpretation of intuitionistic logic by means of atomic polymorphism\, Studia Logica\, 108\, pp. 477-507\, 2020.\ n\n4. J. Espírito Santo\, G. Ferreira\, The Russell-Prawitz embedding and the atomization of universal instantiation\, Logic Journal of the IGPL\, 29(5)\, pp. 823-858\, 2021.\n\n5. J. Espírito Santo\, G. Ferreira\, How t o avoid the commuting conversions of IPC\, Theoretical Computer Science\, 1033\, 2025\n LOCATION:https://researchseminars.org/talk/OLS/190/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Hoyrup (LORIA) DTSTART:20250911T180000Z DTEND:20250911T190000Z DTSTAMP:20260422T225801Z UID:OLS/191 DESCRIPTION:Title: Co mputable type: an overview\nby Mathieu Hoyrup (LORIA) as part of Onlin e logic seminar\n\n\nAbstract\nA compact metrizable space X has computable type if for every set that is homeomorphic to X\, semicomputability is eq uivalent to computability. This notion was first studied by Joe Miller in 2002\, who showed that finite-dimensional spheres all have computable type . It was then developed by Zvonko Iljazović and his co-authors\, who show ed among many other results that compact manifolds also enjoy this propert y. I will present recent results on the notion of computable type\, obtain ed in collaboration with Djamel Eddine Amir during his PhD\, such as: a si mple characterization of 2-dimensional simplicial complexes having computa be type\, a proof that this property is not preserved by taking binary pro ducts.\n LOCATION:https://researchseminars.org/talk/OLS/191/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiang Yin (Imperial College London) DTSTART:20251023T180000Z DTEND:20251023T190000Z DTSTAMP:20260422T225801Z UID:OLS/192 DESCRIPTION:Title: On explaining Quantitative Bipolar Argumentation Frameworks\nby Xiang Yi n (Imperial College London) as part of Online logic seminar\n\n\nAbstract\ nQuantitative Bipolar Argumentation Frameworks (QBAFs) provide a powerful tool for modeling reasoning in various applications such as recommender sy stems and fraud detection. However\, there is limited work on explaining t heir numerical reasoning outcomes in a systematic way. In this talk\, I wi ll present three novel explanation methods tailored for QBAFs. First\, Arg ument Attribution Explanations (AAEs) quantify how much each argument cont ributes to a given outcome. Second\, Relation Attribution Explanations (RA Es) shift the focus from explaining the influence of arguments to the supp ort and attack relations\, offering a more fine-grained view of the reason ing process. Third\, Counterfactual Explanations (CEs) identify changes to the base scores of the arguments that would lead to a different but more desired outcome\, supporting actionable insights and contestability.\n LOCATION:https://researchseminars.org/talk/OLS/192/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Goldberg (University of California Berkeley) DTSTART:20251204T190000Z DTEND:20251204T200000Z DTSTAMP:20260422T225801Z UID:OLS/193 DESCRIPTION:by Gabriel Goldberg (University of California Berkeley) as pa rt of Online logic seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/OLS/193/ END:VEVENT BEGIN:VEVENT SUMMARY:Emma Dinowitz (City University of New York) DTSTART:20251030T180000Z DTEND:20251030T190000Z DTSTAMP:20260422T225801Z UID:OLS/194 DESCRIPTION:Title: A point to set principle for topological entropy and applications to relatin g dimension\, entropy\, and Lyapunov exponents\nby Emma Dinowitz (City University of New York) as part of Online logic seminar\n\n\nAbstract\nWe prove a point to set principle for topological entropy by extending the o rbit complexity framework established by Galatolo\, Hoyrup\, and Rojas. We use this to establish some classical results in dynamical systems relatin g dimension\, entropy\, and Lyapunov exponents\, and prove several new dim ension formulas in the setting of nonuniformly hyperbolic dynamical system s.\n LOCATION:https://researchseminars.org/talk/OLS/194/ END:VEVENT BEGIN:VEVENT SUMMARY:Garrett Ervin (Eötvös Loránd University) DTSTART:20260312T180000Z DTEND:20260312T190000Z DTSTAMP:20260422T225801Z UID:OLS/195 DESCRIPTION:Title: Ne w arithmetic laws for order types\nby Garrett Ervin (Eötvös Loránd University) as part of Online logic seminar\n\n\nAbstract\nLet (LO\, +) de note the class of linear orders equipped with the operation of ordered sum (i.e. concatenation). Despite the enormous diversity of linear order type s\, arithmetic in (LO\, +) is surprisingly nice in certain respects: Linde nbaum showed that (LO\, +) satisfies a completely general Euclidean divisi on theorem\, and Aronszajn found an elegant structural characterization of the commuting pairs in (LO\, +). Yet although these theorems generalize b asic facts about sums of natural numbers\, the published proofs are somewh at difficult and ad hoc. \n\nIn recent work with Eric Paul\, we develop a systematic approach to the arithmetic of (LO\, +) by adapting a structure theory for group actions on linear orders due to McCleary and others. Usin g this approach\, we give new\, unified proofs of Lindenbaum’s and Arons zajn’s theorems. We then generalize this approach to semigroups acting b y convex embeddings on linear orders\, obtain an arithmetic characterizati on of commutativity in (LO\, +)\, and determine exactly the commutative se migroups that can be represented in (LO\, +). I will give an overview of o ur work\, outline some of the proofs\, and discuss future directions.\n LOCATION:https://researchseminars.org/talk/OLS/195/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Mathias DTSTART:20260122T190000Z DTEND:20260122T200000Z DTSTAMP:20260422T225801Z UID:OLS/196 DESCRIPTION:Title: It eration Problems in Symbolic Dynamics I\nby Adrian Mathias as part of Online logic seminar\n\n\nAbstract\nFind abstract and handouts at http://lagr ange.math.siu.edu/calvert/OnlineLogicSeminar.html.\n LOCATION:https://researchseminars.org/talk/OLS/196/ END:VEVENT BEGIN:VEVENT SUMMARY:Linda Lawton (Northern Mighigan University) DTSTART:20260319T180000Z DTEND:20260319T190000Z DTSTAMP:20260422T225801Z UID:OLS/197 DESCRIPTION:Title: De cidability of the AE Theory of $\\Pi^0_1$ Classes$^*$\nby Linda Lawton (Northern Mighigan University) as part of Online logic seminar\n\n\nAbstr act\nClick here for abstract\n LOCATION:https://researchseminars.org/talk/OLS/197/ END:VEVENT BEGIN:VEVENT SUMMARY:Sara Riva (Université de Lille) DTSTART:20260129T190000Z DTEND:20260129T200000Z DTSTAMP:20260422T225801Z UID:OLS/198 DESCRIPTION:Title: Co ntrol and synthesis of minimal trap spaces in Boolean Network\nby Sara Riva (Université de Lille) as part of Online logic seminar\n\n\nAbstract \nSince recent years\, we observe a surge of successful applications of Bo olean networks (BNs) in biology and medicine for the modeling and predicti on of cellular dynamics in the case of cancer and cellular reprogramming. Such applications face two main challenges: being able to design a qualita tive Boolean model which is faithful to the behavior of the biological sys tem and being able to compute predictions to control its (long-term) dynam ics. From a computational point of view\, the latter problem mostly depend s on the complexity of the dynamical property to enforce\, while the forme r additionally suffers from the combinatorics of candidate models.\n\nMini mal trap spaces (MTSs) capture subspaces in which the Boolean dynamics is trapped\, whatever the update mode. They correspond to the attractors of t he most permissive mode. Due to their versatility\, the computation of MTS s has recently gained traction\, essentially by focusing on their enumerat ion. We address the logical reasoning on universal properties of MTSs in t he scope of two problems: the reprogramming of Boolean networks for identi fying the permanent freeze of Boolean variables that enforce a given prope rty on all the MTSs\, and the synthesis of Boolean networks from universal properties on their MTSs. Both problems reduce to solving the satisfiabil ity of quantified propositional logic formula with 3 levels of quantifiers .\n LOCATION:https://researchseminars.org/talk/OLS/198/ END:VEVENT BEGIN:VEVENT SUMMARY:Talk Canceled DTSTART:20260205T190000Z DTEND:20260205T200000Z DTSTAMP:20260422T225801Z UID:OLS/199 DESCRIPTION:Title: Ta lk Canceled\nby Talk Canceled as part of Online logic seminar\n\n\nAbs tract\nWhat does it mean that an event C ``actually caused'' event E?\nThe problem of defining actual causation goes beyond mere philosophical\nspec ulation. For example\, in many legal arguments\, it is precisely what\nne eds to be established in order to determine responsibility. (What exactly \nwas the actual cause of the car accident or the medical problem?)\nThe p hilosophy literature has been struggling with the problem\nof defining cau sality since the days of Hume\, in the 1700s.\nMany of the definitions hav e been couched in terms of counterfactuals.\n(C is a cause of E if\, had C not happened\, then E would not have happened.)\nIn 2001\, Judea Pearl an d I introduced a new definition of actual cause\,\nusing Pearl's notion of structural equations to model\ncounterfactuals. The definition has been revised twice since then\,\nextended to deal with notions like "responsibi lity" and "blame"\, and\napplied in databases and program verification. I survey\nthe last 15 years of work here\, including joint work\nwith Judea Pearl\, Hana Chockler\, and Chris Hitchcock. The talk will be\ncompletel y self-contained.\n LOCATION:https://researchseminars.org/talk/OLS/199/ END:VEVENT BEGIN:VEVENT SUMMARY:Janani Lakshmanan (University of Hawai'i) DTSTART:20260507T180000Z DTEND:20260507T190000Z DTSTAMP:20260422T225801Z UID:OLS/200 DESCRIPTION:by Janani Lakshmanan (University of Hawai'i) as part of Online logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAbs tract: TBA\n LOCATION:https://researchseminars.org/talk/OLS/200/ URL:https://zoom.us/j/122323340 END:VEVENT BEGIN:VEVENT SUMMARY:Hongyu Zhu (University of Wisconsin) DTSTART:20260326T180000Z DTEND:20260326T190000Z DTSTAMP:20260422T225801Z UID:OLS/201 DESCRIPTION:Title: A Complete Bounded Theory with Unbounded Types\nby Hongyu Zhu (Universit y of Wisconsin) as part of Online logic seminar\n\n\nAbstract\nSay a first -order theory is bounded if for some finite $n$\, it is $\\forall_n$-axiom atizable\; Similarly for a type. This notion is closely related to descrip tive complexity and provides a measure of complexity for theories and type s. In an attempt to connect the complexity of theories and that of their t ypes\, we show the existence of a bounded (in fact universal) theory which has an unbounded type. The construction uses trees\, and one key step of the proof is showing the pseudofiniteness of finite-height trees.\n LOCATION:https://researchseminars.org/talk/OLS/201/ END:VEVENT BEGIN:VEVENT SUMMARY:Dhruv Kulshreshtha (University of Wisconsin) DTSTART:20260305T190000Z DTEND:20260305T200000Z DTSTAMP:20260422T225801Z UID:OLS/202 DESCRIPTION:Title: Su rjective cardinals and dually Dedekind finite sets\nby Dhruv Kulshresh tha (University of Wisconsin) as part of Online logic seminar\n\n\nAbstrac t\nAssuming the axiom of choice\, cardinal arithmetic is extremely well-be haved: any two sets are comparable in size\, and there is no infinite stri ctly decreasing sequence of cardinals. Moreover\, for any nonempty sets X and Y\, X injects into Y if and only if Y surjects onto X—so the injecti ve and surjective "orderings" coincide. Without choice\, much of this stru cture breaks down: there may exist incomparable sets and infinite strictly decreasing sequences of cardinals. Although the Cantor-Schröder-Bernstei n theorem ensures that if two sets inject into each other then they are in bijective correspondence\, no analogous result need hold for surjections\ , so the injective and surjective orderings may also no longer agree. In t his talk\, we examine the surjective ordering on sets in the absence of ch oice\, focusing on results that highlight just how bad the situation can b e. We also discuss some results surrounding the surjective well-foundednes s of cardinals. We draw on recent works of Shen and Zhou and on joint work of the speaker with Andreas Blass.\n LOCATION:https://researchseminars.org/talk/OLS/202/ END:VEVENT BEGIN:VEVENT SUMMARY:Jorge Cruz Chapital (University of Trononto) DTSTART:20260212T190000Z DTEND:20260212T200000Z DTSTAMP:20260422T225801Z UID:OLS/203 DESCRIPTION:Title: Co nstruction schemes: Finitizations of guessing principles and their paramet rized forcing axioms.\nby Jorge Cruz Chapital (University of Trononto) as part of Online logic seminar\n\n\nAbstract\nIn this talk\, we survey r ecent developments in the theory of capturing schemes introduced by Todorc evic. We present the capturing axioms CAρ​\, CAΔ​\, and CA\, which m ay be viewed as finite-dimensional analogues of the classical guessing pri nciples Club\, CH\, and Diamond\, respectively. We show that many conseque nces traditionally derived from these guessing principles already follow f rom the capturing axioms\, often with significantly simpler proofs. Finall y\, we introduce parametrized forcing axioms naturally associated with the capturing principles and demonstrate how they can be used to establish th e independence of a strong statement about gaps over ω\, a problem that c annot be settled using either traditional guessing principles or standard forcing axioms.\n LOCATION:https://researchseminars.org/talk/OLS/203/ END:VEVENT BEGIN:VEVENT SUMMARY:Adrian Mathias DTSTART:20260219T190000Z DTEND:20260219T200000Z DTSTAMP:20260422T225801Z UID:OLS/204 DESCRIPTION:Title: It eration problems in symbolic dynamics II\nby Adrian Mathias as part of Online logic seminar\n\n\nAbstract\nFind abstract and handouts at http://lag range.math.siu.edu/calvert/OnlineLogicSeminar.html.\n LOCATION:https://researchseminars.org/talk/OLS/204/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Rosendal (University of Maryland) DTSTART:20260226T190000Z DTEND:20260226T200000Z DTSTAMP:20260422T225801Z UID:OLS/205 DESCRIPTION:Title: Co ordinate systems in Banach spaces and lattices via descriptive set theory< /a>\nby Christian Rosendal (University of Maryland) as part of Online logi c seminar\n\n\nAbstract\nUsing methods of descriptive set theory\, we answ er several questions from the literature regarding different notions of in finite bases in Banach lattices. In particular\, under the assumption of a nalytic determinacy\, every σ-order basis (e_n) for a Banach lattice X=[e _n] is a uniform basis\, and every uniform basis is Schauder. Regarding Ba nach spaces\, we consider filter Schauder bases for Banach spaces\, i.e.\, in which the norm convergence of partial sums is replaced by norm converg ence along some appropriate filter on ℕ. We show that every filter Schau der basis with respect to an analytic filter is also a filter Schauder bas is with respect to a Borel filter. The talk is accessible to a general log ic audience. This is joint work with Antonio Aviles\, Mitchell Taylor and Pedro Tradacete.\n LOCATION:https://researchseminars.org/talk/OLS/205/ END:VEVENT BEGIN:VEVENT SUMMARY:John Baldwin (University of Illinois Chicago) DTSTART:20260402T180000Z DTEND:20260402T190000Z DTSTAMP:20260422T225801Z UID:OLS/206 DESCRIPTION:Title: Ca tegoricity for the inferential $\\omega$-logic and $L_{\\omega_1\\omega}$< /a>\nby John Baldwin (University of Illinois Chicago) as part of Online lo gic seminar\n\n\nAbstract\nAbstract available on seminar web page at http://l agrange.math.siu.edu/calvert/OnlineLogicSeminar.html\n LOCATION:https://researchseminars.org/talk/OLS/206/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriela Laboska (Northwestern University) DTSTART:20260430T180000Z DTEND:20260430T190000Z DTSTAMP:20260422T225801Z UID:OLS/207 DESCRIPTION:Title: So me Computabiity-theoretic and Reverse-mathematical Aspects of Partition Re gularity over Algebraic Structures\nby Gabriela Laboska (Northwestern University) as part of Online logic seminar\n\nInteractive livestream: htt ps://zoom.us/j/122323340\n\nAbstract\nAn inhomogeneous system of linear eq uations over a ring $R$ is partition\nregular if for any finite coloring o f $R$\, the system has a monochromatic\nsolution. In 1933\, Rado showed th at an inhomogeneous system is partition\nregular over $\\mathbb{Z}$ if and only if it has a constant solution.\nFollowing a similar approach\, Bysze wski and Krawczyk showed that the\nresult holds over any integral domain. In 2020\, Leader and Russell\ngeneralized this over any commutative ring $ R$\, with a more direct\nproof than what was previously used. In this talk \, we analyze a theorem by Straus from a computability-theoretic and rever se-mathematical point of view. Straus' theorem has been\nused directly or as a motivation to many of the results in this area.\n LOCATION:https://researchseminars.org/talk/OLS/207/ URL:https://zoom.us/j/122323340 END:VEVENT BEGIN:VEVENT SUMMARY:Stanislav Srednyak (Duke University) DTSTART:20260409T180000Z DTEND:20260409T190000Z DTSTAMP:20260422T225801Z UID:OLS/208 DESCRIPTION:Title: On logical problems arising in atomic and particle physics\nby Stanislav Srednyak (Duke University) as part of Online logic seminar\n\n\nAbstract\ nIn this talk\, I will present certain ideas from quantum field theory tha t lead to mathematical problems typically addressed in mathematical logic literature. This will be an overview talk\, accessible to a general logic audience\, and it will have four main themes:\n\n1) evidence that non comp utable functions arise in dynamics of elementary particles. I will discuss how this non computability can manifest itself in precision measurements and what this means for quantum computing.\n\n2) rigorous definition of pa th integral. I will formulate the problem in the language of Banach space theory\, and discuss relations to recent work on Banach homological algebr a.\n\n3) higher quantizations and higher functionals. I will define a hier archy of symmetric functionals of low complexity but arbitrarily high in t he constructive universe\, and show the relevance of this construction to physical observables.\n\n4) quantum randomness vs mathematical randomness. I will compare these two notions of randomness and discuss what is the in terplay with the hierarchies of definable function spaces and the problem in 2) of defining integration over function spaces. I will touch upon the measurement problem and its interpretation from a mathematical perspective .\n LOCATION:https://researchseminars.org/talk/OLS/208/ END:VEVENT BEGIN:VEVENT SUMMARY:José Jeremías Valenzuela Morales (George Washington University) DTSTART:20260416T180000Z DTEND:20260416T190000Z DTSTAMP:20260422T225801Z UID:OLS/209 DESCRIPTION:Title: A Timeline of Lattice Embeddings into the Turing Degrees\nby José Jerem ías Valenzuela Morales (George Washington University) as part of Online l ogic seminar\n\n\nAbstract\nThe Turing degrees form a rich upper semilatti ce. As such\, a natural way to explore their structure is by studying whic h types of semilattices can be embedded into them. From Kleene-Post's embe ddability result for finite upper semilattices\, to Lerman's embeddability criterion and Montalbán's work on jump upper semilattices\, this exposit ory talk will survey several classic embedding results with a focus on the ir techniques and machinery.\n LOCATION:https://researchseminars.org/talk/OLS/209/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Klatt (George Washington University) DTSTART:20260423T180000Z DTEND:20260423T190000Z DTSTAMP:20260422T225801Z UID:OLS/210 DESCRIPTION:Title: Co hesive powers of Galois extensions\nby Henry Klatt (George Washington University) as part of Online logic seminar\n\nInteractive livestream: htt ps://zoom.us/j/122323340\n\nAbstract\nA cohesive product is a computabilit y theoretic analog to an ultraproduct\, in which the domain is restricted to a collection of partial computable functions\, and the role of the ultr afilter is played by a cohesive set. Unlike the ultraproduct\, the cohesi ve power is always countable\, but it only obeys a fragment of Łoś's the orem. In this talk we discuss recent work with Rumen Dimitrov\, Valentina Harizanov\, and Keshav Srinivasan on the relationship between cohesive pr oducts of various fields and their Automorphism groups to the Galois group s of the base fields.\n LOCATION:https://researchseminars.org/talk/OLS/210/ URL:https://zoom.us/j/122323340 END:VEVENT END:VCALENDAR