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BEGIN:VEVENT
SUMMARY:Mariya Soskova (University of Wisconsin)
DTSTART;VALUE=DATE-TIME:20200423T180000Z
DTEND;VALUE=DATE-TIME:20200423T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200430T180000Z
DTEND;VALUE=DATE-TIME:20200430T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200507T180000Z
DTEND;VALUE=DATE-TIME:20200507T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200514T180000Z
DTEND;VALUE=DATE-TIME:20200514T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200521T180000Z
DTEND;VALUE=DATE-TIME:20200521T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200528T180000Z
DTEND;VALUE=DATE-TIME:20200528T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200604T180000Z
DTEND;VALUE=DATE-TIME:20200604T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200611T180000Z
DTEND;VALUE=DATE-TIME:20200611T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200625T180000Z
DTEND;VALUE=DATE-TIME:20200625T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200709T180000Z
DTEND;VALUE=DATE-TIME:20200709T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200618T180000Z
DTEND;VALUE=DATE-TIME:20200618T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200716T180000Z
DTEND;VALUE=DATE-TIME:20200716T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200723T180000Z
DTEND;VALUE=DATE-TIME:20200723T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200702T180000Z
DTEND;VALUE=DATE-TIME:20200702T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200730T180000Z
DTEND;VALUE=DATE-TIME:20200730T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200806T180000Z
DTEND;VALUE=DATE-TIME:20200806T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200813T180000Z
DTEND;VALUE=DATE-TIME:20200813T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200820T180000Z
DTEND;VALUE=DATE-TIME:20200820T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200910T180000Z
DTEND;VALUE=DATE-TIME:20200910T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200903T180000Z
DTEND;VALUE=DATE-TIME:20200903T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200827T180000Z
DTEND;VALUE=DATE-TIME:20200827T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200917T180000Z
DTEND;VALUE=DATE-TIME:20200917T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201001T180000Z
DTEND;VALUE=DATE-TIME:20201001T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201119T190000Z
DTEND;VALUE=DATE-TIME:20201119T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20200924T180000Z
DTEND;VALUE=DATE-TIME:20200924T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201203T190000Z
DTEND;VALUE=DATE-TIME:20201203T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210121T190000Z
DTEND;VALUE=DATE-TIME:20210121T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210114T190000Z
DTEND;VALUE=DATE-TIME:20210114T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201022T180000Z
DTEND;VALUE=DATE-TIME:20201022T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201112T190000Z
DTEND;VALUE=DATE-TIME:20201112T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201029T180000Z
DTEND;VALUE=DATE-TIME:20201029T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210204T190000Z
DTEND;VALUE=DATE-TIME:20210204T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201105T190000Z
DTEND;VALUE=DATE-TIME:20201105T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201015T180000Z
DTEND;VALUE=DATE-TIME:20201015T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201008T180000Z
DTEND;VALUE=DATE-TIME:20201008T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20201210T190000Z
DTEND;VALUE=DATE-TIME:20201210T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210128T190000Z
DTEND;VALUE=DATE-TIME:20210128T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210218T190000Z
DTEND;VALUE=DATE-TIME:20210218T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210415T180000Z
DTEND;VALUE=DATE-TIME:20210415T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210211T190000Z
DTEND;VALUE=DATE-TIME:20210211T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210304T190000Z
DTEND;VALUE=DATE-TIME:20210304T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210225T190000Z
DTEND;VALUE=DATE-TIME:20210225T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210325T180000Z
DTEND;VALUE=DATE-TIME:20210325T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210311T190000Z
DTEND;VALUE=DATE-TIME:20210311T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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\
n*abelian* 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;VALUE=DATE-TIME:20210401T180000Z
DTEND;VALUE=DATE-TIME:20210401T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210429T180000Z
DTEND;VALUE=DATE-TIME:20210429T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210506T180000Z
DTEND;VALUE=DATE-TIME:20210506T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210520T180000Z
DTEND;VALUE=DATE-TIME:20210520T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210422T180000Z
DTEND;VALUE=DATE-TIME:20210422T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210513T180000Z
DTEND;VALUE=DATE-TIME:20210513T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210527T180000Z
DTEND;VALUE=DATE-TIME:20210527T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210708T180000Z
DTEND;VALUE=DATE-TIME:20210708T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210617T180000Z
DTEND;VALUE=DATE-TIME:20210617T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210909T180000Z
DTEND;VALUE=DATE-TIME:20210909T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210819T180000Z
DTEND;VALUE=DATE-TIME:20210819T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210610T180000Z
DTEND;VALUE=DATE-TIME:20210610T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210603T180000Z
DTEND;VALUE=DATE-TIME:20210603T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210701T180000Z
DTEND;VALUE=DATE-TIME:20210701T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210715T180000Z
DTEND;VALUE=DATE-TIME:20210715T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210902T180000Z
DTEND;VALUE=DATE-TIME:20210902T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210729T180000Z
DTEND;VALUE=DATE-TIME:20210729T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210826T180000Z
DTEND;VALUE=DATE-TIME:20210826T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210722T180000Z
DTEND;VALUE=DATE-TIME:20210722T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211021T180000Z
DTEND;VALUE=DATE-TIME:20211021T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211028T180000Z
DTEND;VALUE=DATE-TIME:20211028T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210916T180000Z
DTEND;VALUE=DATE-TIME:20210916T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211014T180000Z
DTEND;VALUE=DATE-TIME:20211014T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211118T190000Z
DTEND;VALUE=DATE-TIME:20211118T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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\nIn this talk\, I will:\n

\n- Introduc
e John Eliot and the linguistic context he was working in.Introd
uce the contents of the
*Logick Primer*---vocabulary\, inference patt
erns\, and applications. \n- Discuss notions of ``Puritan'' logic th
at inform this primer.
\n- Talk about the importance of his work in
documenting and expanding the Massachusett language and the problems that
accompany his colonial approach to this work.

\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;VALUE=DATE-TIME:20211111T190000Z
DTEND;VALUE=DATE-TIME:20211111T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211104T180000Z
DTEND;VALUE=DATE-TIME:20211104T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211007T180000Z
DTEND;VALUE=DATE-TIME:20211007T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211202T190000Z
DTEND;VALUE=DATE-TIME:20211202T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20210930T180000Z
DTEND;VALUE=DATE-TIME:20210930T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211209T190000Z
DTEND;VALUE=DATE-TIME:20211209T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20211216T190000Z
DTEND;VALUE=DATE-TIME:20211216T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220127T190000Z
DTEND;VALUE=DATE-TIME:20220127T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220113T190000Z
DTEND;VALUE=DATE-TIME:20220113T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220120T190000Z
DTEND;VALUE=DATE-TIME:20220120T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220224T190000Z
DTEND;VALUE=DATE-TIME:20220224T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220303T190000Z
DTEND;VALUE=DATE-TIME:20220303T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220210T190000Z
DTEND;VALUE=DATE-TIME:20220210T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220317T180000Z
DTEND;VALUE=DATE-TIME:20220317T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220428T180000Z
DTEND;VALUE=DATE-TIME:20220428T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220324T180000Z
DTEND;VALUE=DATE-TIME:20220324T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220331T180000Z
DTEND;VALUE=DATE-TIME:20220331T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220414T180000Z
DTEND;VALUE=DATE-TIME:20220414T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220505T180000Z
DTEND;VALUE=DATE-TIME:20220505T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221215T190000Z
DTEND;VALUE=DATE-TIME:20221215T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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 Misesâ€™ 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;VALUE=DATE-TIME:20220818T180000Z
DTEND;VALUE=DATE-TIME:20220818T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221027T180000Z
DTEND;VALUE=DATE-TIME:20221027T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220825T180000Z
DTEND;VALUE=DATE-TIME:20220825T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220901T180000Z
DTEND;VALUE=DATE-TIME:20220901T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220908T180000Z
DTEND;VALUE=DATE-TIME:20220908T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220915T180000Z
DTEND;VALUE=DATE-TIME:20220915T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221103T180000Z
DTEND;VALUE=DATE-TIME:20221103T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221013T180000Z
DTEND;VALUE=DATE-TIME:20221013T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221020T180000Z
DTEND;VALUE=DATE-TIME:20221020T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20220922T180000Z
DTEND;VALUE=DATE-TIME:20220922T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221110T190000Z
DTEND;VALUE=DATE-TIME:20221110T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221117T190000Z
DTEND;VALUE=DATE-TIME:20221117T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20221201T190000Z
DTEND;VALUE=DATE-TIME:20221201T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230119T190000Z
DTEND;VALUE=DATE-TIME:20230119T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230216T190000Z
DTEND;VALUE=DATE-TIME:20230216T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230202T190000Z
DTEND;VALUE=DATE-TIME:20230202T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230126T190000Z
DTEND;VALUE=DATE-TIME:20230126T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230302T190000Z
DTEND;VALUE=DATE-TIME:20230302T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230323T180000Z
DTEND;VALUE=DATE-TIME:20230323T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230504T180000Z
DTEND;VALUE=DATE-TIME:20230504T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230316T180000Z
DTEND;VALUE=DATE-TIME:20230316T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230209T190000Z
DTEND;VALUE=DATE-TIME:20230209T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230427T180000Z
DTEND;VALUE=DATE-TIME:20230427T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230406T180000Z
DTEND;VALUE=DATE-TIME:20230406T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230223T190000Z
DTEND;VALUE=DATE-TIME:20230223T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230511T180000Z
DTEND;VALUE=DATE-TIME:20230511T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230330T180000Z
DTEND;VALUE=DATE-TIME:20230330T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230914T180000Z
DTEND;VALUE=DATE-TIME:20230914T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231102T180000Z
DTEND;VALUE=DATE-TIME:20231102T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231005T180000Z
DTEND;VALUE=DATE-TIME:20231005T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231026T180000Z
DTEND;VALUE=DATE-TIME:20231026T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231207T190000Z
DTEND;VALUE=DATE-TIME:20231207T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230824T180000Z
DTEND;VALUE=DATE-TIME:20230824T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230907T180000Z
DTEND;VALUE=DATE-TIME:20230907T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230921T180000Z
DTEND;VALUE=DATE-TIME:20230921T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231019T180000Z
DTEND;VALUE=DATE-TIME:20231019T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231109T190000Z
DTEND;VALUE=DATE-TIME:20231109T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230928T180000Z
DTEND;VALUE=DATE-TIME:20230928T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231116T190000Z
DTEND;VALUE=DATE-TIME:20231116T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231130T190000Z
DTEND;VALUE=DATE-TIME:20231130T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231214T190000Z
DTEND;VALUE=DATE-TIME:20231214T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20230831T180000Z
DTEND;VALUE=DATE-TIME:20230831T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20231012T180000Z
DTEND;VALUE=DATE-TIME:20231012T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240411T180000Z
DTEND;VALUE=DATE-TIME:20240411T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240118T190000Z
DTEND;VALUE=DATE-TIME:20240118T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240201T190000Z
DTEND;VALUE=DATE-TIME:20240201T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240509T180000Z
DTEND;VALUE=DATE-TIME:20240509T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240215T190000Z
DTEND;VALUE=DATE-TIME:20240215T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240208T190000Z
DTEND;VALUE=DATE-TIME:20240208T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240314T180000Z
DTEND;VALUE=DATE-TIME:20240314T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240328T180000Z
DTEND;VALUE=DATE-TIME:20240328T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240307T190000Z
DTEND;VALUE=DATE-TIME:20240307T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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 2^{c} 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 2^{c} 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;VALUE=DATE-TIME:20240926T180000Z
DTEND;VALUE=DATE-TIME:20240926T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240425T180000Z
DTEND;VALUE=DATE-TIME:20240425T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240502T180000Z
DTEND;VALUE=DATE-TIME:20240502T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20241024T180000Z
DTEND;VALUE=DATE-TIME:20241024T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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\nInteractive l
ivestream: https://zoom.us/j/122323340\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 copies $\\mathcal{B}$ of
$\\mathcal{A}$\, there exists a $\\mathbf{d}$-computable isomorphism betw
een $\\mathcal{A}$ and $\\mathcal{B}$. In 2021 result by Downey\, Harrison
-Trainor\, and Melnikov\, it was shown that there exists a computable grap
h $\\mathcal{G}$ such that for an infinite increasing sequence of c.e.\\ d
egrees $\\mathbf{x}_0 <_T \\mathbf{y}_0 <_T \\mathbf{x}_1 <_T \\mathbf{y}_
1\\dots$\, $\\mathcal{G}$ was computably categorical relative to each $\\m
athbf{x}_i$ but not computably categorical relative to each $\\mathbf{y}_i
$. That is\, the behavior of categoricity relative to a degree is not mo
notonic under $\\mathbf{0}'$. In this talk\, we will sketch how to extend
this result for partial orders of c.e.\\ degrees\, and discuss some future
directions of this project.\n
LOCATION:https://researchseminars.org/talk/OLS/155/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jinhe Ye (University of Oxford)
DTSTART;VALUE=DATE-TIME:20241010T180000Z
DTEND;VALUE=DATE-TIME:20241010T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20240912T180000Z
DTEND;VALUE=DATE-TIME:20240912T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20241121T190000Z
DTEND;VALUE=DATE-TIME:20241121T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
UID:OLS/158
DESCRIPTION:by Julia Knight (Notre Dame) as part of Online logic seminar\n
\nInteractive livestream: https://zoom.us/j/122323340\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OLS/158/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles McCoy (University of Portland)
DTSTART;VALUE=DATE-TIME:20241107T190000Z
DTEND;VALUE=DATE-TIME:20241107T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
UID:OLS/159
DESCRIPTION:by Charles McCoy (University of Portland) as part of Online lo
gic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/OLS/159/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dicle Mutlu (McMaster University)
DTSTART;VALUE=DATE-TIME:20241114T190000Z
DTEND;VALUE=DATE-TIME:20241114T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
UID:OLS/160
DESCRIPTION:by Dicle Mutlu (McMaster University) as part of Online logic s
eminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/OLS/160/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sunil Karn (Southern Illinois University)
DTSTART;VALUE=DATE-TIME:20241205T190000Z
DTEND;VALUE=DATE-TIME:20241205T200000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
UID:OLS/161
DESCRIPTION:by Sunil Karn (Southern Illinois University) as part of Online
logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/OLS/161/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Don Stull (University of Chicago)
DTSTART;VALUE=DATE-TIME:20241003T180000Z
DTEND;VALUE=DATE-TIME:20241003T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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;VALUE=DATE-TIME:20241031T180000Z
DTEND;VALUE=DATE-TIME:20241031T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
UID:OLS/163
DESCRIPTION:by Janani Lakshmanan (University of Hawaii) as part of Online
logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/OLS/163/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Sanders (RUB Bochum)
DTSTART;VALUE=DATE-TIME:20241017T180000Z
DTEND;VALUE=DATE-TIME:20241017T190000Z
DTSTAMP;VALUE=DATE-TIME:20241016T070143Z
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\nInteractive livestrea
m: https://zoom.us/j/122323340\n\nAbstract\nThe study of (compact) metric
spaces in second-order Reverse Mathematics (RM hereafter) is fundamentally
based on separability conditions\, while the latter are generally avoided
in proof mining to enable the extraction of good computational data. Insp
ired by this observation\, we study basic properties of ‘unrepresented
’ compact metric spaces in Kohlenbach’s higher-order RM\, i.e. we do n
ot assume separability conditions. Our results are four-fold as follows\,
each building on the next.\n\nMost definitions of compactness yield third-
order theorems not provable from second-order comprehension axioms. Only o
ne very specific choice of compactness definitions yields equivalences inv
olving the so-called Big Five of second-order RM.\n\nMany basic properties
of compact metric spaces inhabit the range of hyperarithmetical analysis.
Until recently\, few natural examples of the latter were known.\n\nSome b
asic properties of compact metric spaces\, like the intermediate value the
orem\, are equivalent to countable choice as studied in higher-order RM\,
namely QF-AC0\,1.\n\nSome basic properties of compact metric spaces\, like
a continuous function has a supremum and a countable set has measure zero
\, imply strong axioms including Feferman’s projection principle\, full
second-order arithmetic\, and Kleene’s quantifier (∃3).\n\nIn conclusi
on\, the removal of separability conditions from compact metric spaces res
ults in rather interesting phenomena.\n
LOCATION:https://researchseminars.org/talk/OLS/164/
URL:https://zoom.us/j/122323340
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