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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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
UID:OLS/57
DESCRIPTION:by Marcelo Arena (Pontificia Universidad Católica de Chile) a
s part of Online logic seminar\n\nInteractive livestream: https://zoom.us/
j/122323340\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OLS/57/
URL:https://zoom.us/j/122323340
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:20210804T220733Z
UID:OLS/58
DESCRIPTION:by Joel Nagloo (University of Illinois Chicago) as part of Onl
ine logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\n
Abstract: TBA\n
LOCATION:https://researchseminars.org/talk/OLS/58/
URL:https://zoom.us/j/122323340
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
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:20210804T220733Z
UID:OLS/64
DESCRIPTION:by Cristina Sernadas (Universidade de Lisbona) as part of Onli
ne logic seminar\n\nInteractive livestream: https://zoom.us/j/122323340\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/OLS/64/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Spink (Stanford)
DTSTART;VALUE=DATE-TIME:20210729T180000Z
DTEND;VALUE=DATE-TIME:20210729T190000Z
DTSTAMP;VALUE=DATE-TIME:20210804T220733Z
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:20210804T220733Z
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\nInteractive l
ivestream: https://zoom.us/j/122323340\n\nAbstract\nIn 2005\, Kechris\, Pe
stov and Todorcevic exhibited a\ncorrespondence between combinatorial prop
erties of structures and\ndynamical properties of their automorphism group
s. In 2012\, Angel\,\nKechris and Lyons used this correspondence to show t
he unique ergodicity\nof all the minimal actions of some subgroups of $S_\
\infty$. In this\ntalk\, I will give an overview of the aforementioned res
ults and discuss\nrecent work generalizing results of Angel\, Kechris and
Lyons in several\ndirections.\n
LOCATION:https://researchseminars.org/talk/OLS/66/
URL:https://zoom.us/j/122323340
END:VEVENT
BEGIN:VEVENT
SUMMARY:Noah Schweber (Proof School)
DTSTART;VALUE=DATE-TIME:20210722T180000Z
DTEND;VALUE=DATE-TIME:20210722T190000Z
DTSTAMP;VALUE=DATE-TIME:20210804T220733Z
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
END:VCALENDAR