Online Activities 19-25 April

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 19 April, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Francois Le Maitre, University of Paris
Title: A characterization of high transitivity for groups acting on trees
Abstract: A countable group is highly transitive if it admits an embedding in the permutation group of the integers with dense image. I will present a joint work with Pierre Fima, Soyoung Moon and Yves Stalder where we show that a large class of groups acting on trees are highly transitive, which yields a characterization of high transitivity for groups admitting a minimal faithful action of general type on a tree thanks to the work of Le Boudec and Matte Bon. Our proof is new even for the free group on two generators and I will give a detailed overview in this very particular case, showing that the generic transitive action of the free group on two generators is highly transitive.
Information: Check on the seminar webpage if the seminar will take place.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 21 April, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Omer Ben Neria
Title: Strong Prikry property for Magidor Iterations
Abstract: In his celebrated work on the identity crisis of strongly compact cardinals, Magidor introduced a special iteration of Prikry forcings for a set of measurable cardinals, known as the Magidor iteration.The purpose of this talk is to state and prove a version of the strong Prikry Lemma for such iterations, extending a result of Fuchs for the case where the set of measurables is discrete.  We will also describe several applications regarding the genericity of sequences of critical points in iterated ultrapowers.
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 21 April, 15:15-16:45 CET
Speaker: tba
Title: tba
Abstract: tba
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Barcelona Set Theory Seminar
Time: Wednesday, 21 April, 16:00-17:30 CET
Speaker: Sam Roberts
Title: Reinhardt’s potentialism
Abstract: Reflection principles have been of interest to philosophers and mathematicians because they promise to be well-motivated additions to the standard axioms of set theory that nonetheless settle many of the questions left open by those axioms. Although William Reinhardt’s work on reflection principles has been immensely influential, some of his central ideas have remained unclear. The purpose of my talk will be to rectify this. I will start by outlining and formalising his primary contribution to the literature on reflection principles, which is a version of potentialism. I will then show that it is remarkably strong and discuss a number of criticisms.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

KGRC Research Seminar, Vienna
Time: Thursday, 22 April, 15:00-16:30 CET
Speaker: Osvaldo Guzmán, Universidad Nacional Autónoma de México
Title: MAD families and strategically bounding forcings
Abstract: The notion of strategically bounding forcings is a natural game-theoretic strengthening of the bounding  property for partial orders.  In this talk, we will study the basic properties of strategically bounding forcings and talk about indestructibility of MAD families. The motivation for this work is the problem of Roitman.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 23 April, 16:30-18:30 CET
Speaker: F. Loregian, Tallinn University of Technology
Title: Functorial Semantics for Partial Theories
Abstract: We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of string diagrams as terms. This allows for equational reasoning about the class of models defined by a partial theory. We demonstrate the expressivity of such equational theories by considering a number of examples, including partial combinatory algebras and cartesian closed categories. Moreover, despite the increase in expressivity of the syntax we retain a well-behaved notion of semantics: we show that our categories of models are precisely locally finitely presentable categories, and that free models exist.
Information: Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 23 April, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 23 April, 2pm New York time (20:00 CET)
Speaker: Andres Villaveces, CUNY
Title: Two logics, and their connections with large cardinals / Questions for BDGM: Part II
Abstract: In the past couple of years I have been involved (joint work with Väänänen and independently with Shelah) with some logics in the vicinity of Shelah’s L1κ (a logic from 2012 that has Interpolation and a very weak notion of compactness, namely Strong Undefinability of Well-Orderings, and in some cases has a Lindström-type theorem for those two properties). Our work with Väänänen weakens the logic but keeps several properties. Our work with Shelah explores the connection with definability of AECs.
These logics seem to have additional interesting properties under the further assumption of strong compactness of a cardinal, and this brings them close to recent work of Boney, Dimopoulos, Gitman and Magidor [BDGM].
During the first lecture, I plan to describe two games and a syntax of two logics: Shelah’s L1κ and my own logic (joint work with Väänänen) L1,cκ. I will stress some of the properties of these logics, without any use of large cardinal assumptions. During the second lecture, I plan to enter rather uncharted territory. I will describe some constructions done by Shelah (mostly) under the assumption of strong compactness, but I also plan to bring these logics to a territory closer to the work of [BDGM]. This second lecture will have more conjectures, ideas, and (hopefully interesting) discussions with some of the authors of that paper.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

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13th Panhellenic Logic Symposium postponed to 2022

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PLS13: THE THIRTEENTH PANHELLENIC LOGIC SYMPOSIUM
Postponed to: July 2022, Volos, Greece
Organized by the University of Thessaly
http://panhellenic-logic-symposium.org/

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IMPORTANT UPDATE:

– The meeting is postponed to July 2022, due to the uncertainties related to the pandemic. Exact dates will be decided at a later stage.

– Currently submitted papers will be reviewed according to this year’s schedule.

– Accepted papers will be announced per schedule this year and will be
included in the online proceedings. The submission and notification
process will be repeated next year.

– The authors of accepted papers this year have the options to:

(a) Send us this year a pre-recorded video of their presentation which will be posted on our webpage and also present live next year during the actual event 

(b) Present directly during the actual event in 2022

======================================================================

SUBMISSION DATES

Submission and review process has closed and will be repeated next
year, around spring 2022.

======================================================================

Tentative list of speakers – July 2022

INVITED TALKS

– Andrew Brooke-Taylor, University of Leeds, UK
– Takayuki Kihara, Nagoya University, Japan
– Julia Knight, University of Notre Dame, USA
– Vassileios Koutavas, Trinity College Dublin, Ireland
– Angus Macintyre, Queen Mary University of London, UK
– Thanases Pheidas, University of Crete, Greece
– Alexandra Silva, University College London, UK
– Linda Brown Westrick, Penn State University, USA

TUTORIALS

– Alex Kavvos, University of Bristol, UK
– Nikos Leonardos, University of Athens, Greece
– Stathis Zachos, National Technical University of Athens, Greece

SPECIAL SESSIONS

Computer Science:

– Bruno Bauwens, HSE University, Russia
– Juan Garay, Texas A&M University, USA
– Andrew Lewis-Pye, London School of Economics, UK
– Vassilis Zikas, Purdue University, USA & University of Edinburgh, UK

Philosophical Logic:

– Michael Glanzberg, Rutgers University, USA
– Volker Halbach, University of Oxford, UK
– Elia Zardini, University of Lisbon, Portugal & HSE University, Russia

=====================================================================

SECOND CALL FOR PAPERS

The second call is postponed to 2022, as is the actual event. The
articles received during the first call will be reviewed per previous
schedule, the authors will be notified and accepted papers will be
included in the online proceedings this year. The submission and
notification process will be repeated in 2022.

The authors of accepted papers this year have the options to:

(a) Send us this year a pre-recorded video of their presentation which will be posted on our webpage and also present live next year during the actual event  

(b) Present directly during the actual event in 2022

Accepted papers will appear in the electronic volume of the event’s
(informal) proceedings; the volume will be posted on the event’s
webpage.

Areas of interest include (but are not limited to):

– Computability Theory
– History and Philosophy of Logic
– Logic in Computer Science
– Model Theory
– Nonclassical and Modal Logics
– Proof Theory
– Set Theory

Papers, in PDF format, should be prepared using the EasyChair class
style (easychair.org/publications/for_authors), be written in English,
and adhere to a space limit of 6 pages.

Submission is done by EasyChair at:

https://www.easychair.org/my/conference?conf=pls2021

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POSTER SESSION AND MENTORING SESSION (July 2022)

Graduate students and young researchers will be invited to submit a
short abstract on work in progress that may not be ready for a regular
contributed talk. Those accepted will be able to present their work in
poster form in a special poster session. The session will also feature
a mentoring component whereby senior researchers will discuss the
posters and provide feedback to student participants.

The submission of abstracts is postponed to 2022.

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GRANTS

Limited travel grants will be available for students and young researchers
– see the webpage.

=====================================================================

SCIENTIFIC COMMITTEE

– Antonis Achilleos, Reykjavik University
– George Barmpalias, Chinese Academy of Sciences (co-chair)
– Costas Dimitracopoulos, University of Athens
– Pantelis Eleftheriou, University of Konstanz & University of Pisa
– Vassilis Gregoriades, National Technical University of Athens
– Kostas Hatzikiriakou, University of Thessaly
– Antonis Kakas, University of Cyprus
– Alex Kavvos, University of Bristol
– Nikolaos Papaspyrou, National Technical University of Athens
– Thanases Pheidas, University of Crete
– Rizos Sklinos, Stevens Institute of Technology
– Ana Sokolova, University of Salzburg
– Alexandra Soskova, Sofia University
– Mariya Soskova, University of Wisconsin–Madison
– Yannis Stephanou, University of Athens
– Konstantinos Tsaprounis, University of the Aegean (co-chair)
– Nikos Tzevelekos, Queen Mary University of London
– Niki Vazou, IMDEA Institute
– Stathis Zachos, National Technical University of Athens

ORGANIZING COMMITTEE

– Kostas Hatzikiriakou, University of Thessaly (chair)
– Nikolaos Papaspyrou, National Technical University of Athens
– Vasiliki Papayiannakopoulou, University of Thessaly

======================================================================

SYMPOSIUM WEBPAGE: http://panhellenic-logic-symposium.org/
E-MAIL: pls13@softlab.ntua.gr

CONTACTS:

Chairs of the Scientific Committee:

– George Barmpalias (barmpalias@gmail.com)
– Konstantinos Tsaprounis (kostas.tsap@gmail.com)

Chair of the Organizing Committee: 

– Kostas Hatzikiriakou (kxatzkyr@uth.gr)

======================================================================

SPONSORS

The event is supported by the following sources:

– Association for Symbolic Logic (https://aslonline.org)
– European Mathematical Society (https://euro-math-soc.eu)
– Foundation Compositio Mathematica (https://compositio.nl)
– University of Thessaly (https://www.uth.gr/)
– University of Cyprus (http://www.ucy.ac.cy/en/)

======================================================================

Online Activities 12-18 April

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 12 April, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Riccardo Camerlo, University of Genoa
Title: The Wadge hierarchy on Zariski topologies
Abstract: In this talk I will discuss the structure of the relation of continuous reducibility on affine varieties. If time permits, I will also present some results on polynomial reducibility. The results are joint work with C. Massaza.
Information: See the seminar webpage.

Paris-Lyon Séminaire de Logique
Time: Wednesday, 24 March, 16:00-17:00 CET
Speaker: Joel Hamkins, University of Oxford
Title: Determinacy for proper class games
Abstract: The principle of open determinacy for class games — two-player games of perfect information with plays of length ω, where the moves are chosen from a possibly proper class, such as games on the ordinals — is not provable in Zermelo-Fraenkel set theory ZFC or Gödel-Bernays set theory GBC, if these theories are consistent, because provably in ZFC there is a definable open proper class game with no definable winning strategy. In fact, the principle of open determinacy and even merely clopen determinacy for class games implies Con(ZFC) and iterated instances Con(Con(ZFC)) and more, because it implies that there is a satisfaction class for first-order truth, and indeed a transfinite tower of truth predicates for iterated truth-about-truth, relative to any class parameter. This is perhaps explained, in light of the Tarskian recursive definition of truth, by the more general fact that the principle of clopen determinacy is exactly equivalent over GBC to the principle of elementary transfinite recursion ETR over well-founded class relations. Meanwhile, the principle of open determinacy for class games is strictly stronger, although it is provable in the stronger theory GBC+ Pi^1_1-comprehension, a proper fragment of Kelley-Morse set theory KM.
http://jdh.hamkins.org/determinacy-for-proper-class-games-seminaire-de-logique-lyon-paris-april-2021/
Information: Join via the link on the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 14 April, 16:00-17:30 CET
Speaker: Erin Carmody, Fordham University
Title: The relationships between measurable and strongly compact cardinals
Abstract: This talk is about the ongoing investigation of the relationships
between measurable and strongly compact cardinals. I will present some of
the history of the theorems in this theme, including Magidor’s identity crisis,
and give new results. The theorems presented are in particular about the
relationships between strongly compact cardinals and measurable cardinals
of different Mitchell orders. One of the main theorems is that there is a
universe where k1 and k2 are the first and second strongly compact cardinals,
respectively, and where k1 is least with Mitchell order 1, and k2 is the least
with Mitchell order 2. Another main theorem is that there is a universe where
k1 and k2 are the first and second strongly compact cardinals,
respectively, with k1 the least measurable cardinal such that o(k1) = 2 and k2
the least measurable cardinal above k1. This is a joint work in progress with
Victoria Gitman and Arthur Apter.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Ghent-Leeds Virtual Logic Seminar
Time: Thursday, 8 April, 2pm UK time (15:00 CET)
Speaker: Adrian R. D. Mathias, LIM, Université de la Réunion
Title: The eternal question: Where should definitions go? Part 2: The logophilia of economists
Abstract: This enquiry was prompted by a discussion at the BLC meeting in Edinburgh in 2016 and has led me to pursue two themes:
– the fear of logic evinced by many mathematicians
– the strong interest in logic evinced by many economist.
I shall give many examples of the first in the first talk, and of the second in the second The ideas of Husserl illuminate the relationship of economics to mathematics and logic. The Campanella principle (1590?) is that definitions should be at the beginning for teaching but at the end for research. The Humboldt principle (1810) is that in universities, teaching and research should be done by the same people. There is a hint of contradiction here, but the aim of teaching future researchers is to build confidence as well as to transmit learning.
Information: Please contact Paul Shafer in advance to participate.

KGRC Research Seminar, Vienna
Time: Thursday, 15 April, 15:00-16:30 CET
Speaker: Andreas Blass, University of Michigan
Title: Choice, Groups, and Topoi
Abstract: Work of Tarski, Mostowski, Gauntt, and Truss provides finite, group-theoretic criteria for ZF-provability of implications between weak choice axioms of the form “every family of n-element sets has a choice function” or “every countable family of n-element sets has a choice function.”  From a sufficiently broad, category-theoretic viewpoint, these implications and the equivalent group-theoretic criteria look like exactly the same statements but interpreted in different categories, namely certain particular sorts of topoi. The main result is that this equivalence applies not only to these particular sorts of topoi but to all topoi. I plan to describe the ingredients of this work — choice principles, group properties, and topoi — and, if time permits, give a hint about the ideas in the proofs.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 16 April, 16:30-18:30 CET
Speaker: Alejandro Poveda, Hebrew University of Jerusalem
Title: Forcing iterations around singulars cardinals and an application to stationary reflection
Abstract: In this talk we will give an overview of the theory of \Sigma-Prikry forcings and their iterations, recently introduced in a series of papers. We will begin motivating the class of \Sigma-Prikry forcings and showing that this class is broad enough to encompass many Prikry-type posets that center on countable cofinalities. Afterwards, we will present a viable iteration scheme for this family and discuss an application of the framework to the investigation of stationary reflection at the level of successors of singular cardinals. This is joint work with A. Rinot and D. Sinapova.
Information: Online on WebEx. Please see the seminar webpage.

Münster research seminar on set theory
Time: Friday, 16 April, 10:00-12:00 CET (Unusual time!)
Speaker: Liang Yu (Nanjing University).
Title: A basis theorem for Π11-sets.
Abstract: It was claimed by Harrington, but never published, that every non-thin Π11-set ranges over an upper cone of hyperarithmetic degrees. We shall give a proof via a full approximation argument.
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Toronto Set Theory Seminar
Time: Friday, 16 April, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: Micheal Hrusak
Title: Ultrafiters, MAD families and the Katetov order
Abstract: We shall survey recent results concerning classification of MAD 
families and ultrafilters using the Katetov order, concentrating on 
open problems.
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 16 April, 2pm New York time (20:00 CET)
Speaker: Andres Villaveces, CUNY
Title: tba
Abstract: tba
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 5-11 April

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 5 April, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Justin Moore, Cornell University
Title: Subgroups of PLoIPLo⁡I which do not embed into Thompson’s group 
Abstract: The group PLoIPLo⁡I of piecewise linear orientation preserving homeomorphisms of the unit interval, equipped with composition, has a rich array of finitely generated subgroups. A basic question one can ask is when one of these groups embeds into another. One group which seems to play a particularly important role in this quasi-order is Richard Thompson’s group FF. For instance it is conjectured that every finitely generated subgroup of PLoIPLo⁡I either contains a copy of FF or else embeds into FF. I will describe a general dynamical criterion for when a subgroup of PLoIPLo⁡I does not embed into FF which covers all known examples. This is joint work with James Hyde.
Information: See the seminar webpage.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 7 April, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Omer Ben Neria
Title: Strong Prikry Property for Magidor Iterations
Abstract: In his celebrated work on the identity crisis of strongly compact cardinals, Magidor introduced a special iteration of Prikry forcings for a set of measurable cardinals, known as the Magidor iteration. 
The purpose of this talk is to state and prove a version of the strong Prikry Lemma for such iterations, extending a result of Fuchs for the case where the set of measurables is discrete.  We will also describe several applications regarding the genericity of sequences of critical points in iterated ultrapowers.
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Barcelona Set Theory Seminar
Time: Wednesday, 7 April, 16:00-17:30 CET
Speaker: Farmer Schlutzenberg, University of Münster
Title: Some results on restricted mantles
Abstract: Recall that a ground of the set theoretic universe V is a class W
modelling ZFC, such that V is a set-generic extension of W. The mantle M is
the intersection of all grounds. By restricting the size or kind of forcings
permitted, one obtains variants of the mantle, intermediate between M and V.
We will discuss some work on such restricted mantles M’, with some general
results on partial choice principles in M’, and an analysis of certain M’
assuming that V=L[x] for x a real of high complexity; we will also discuss a
restriction on the nature of possible grounds of mice L[E].
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Ghent-Leeds Virtual Logic Seminar
Time: Thursday, 8 April, 2pm UK time (15:00 CET)
Speaker: Adrian R. D. Mathias, LIM, Université de la Réunion
Title: The eternal question: Where should definitions go? Part 1: The logophobia of mathematicians
Abstract: This enquiry was prompted by a discussion at the BLC meeting in Edinburgh in 2016 and has led me to pursue two themes:
– the fear of logic evinced by many mathematicians
– the strong interest in logic evinced by many economist.
I shall give many examples of the first in the first talk, and of the second in the second The ideas of Husserl illuminate the relationship of economics to mathematics and logic. The Campanella principle (1590?) is that definitions should be at the beginning for teaching but at the end for research. The Humboldt principle (1810) is that in universities, teaching and research should be done by the same people. There is a hint of contradiction here, but the aim of teaching future researchers is to build confidence as well as to transmit learning.
Information: Please contact Paul Shafer in advance to participate.

Turin-Udine logic seminar
Time: Friday, 9 April, 16:30-18:30 CET
Speaker: A. Berarducci, University of Pisa
Title: Asymptotic analysis of Skolem’s exponential functions
Abstract: Skolem (1956) studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant 1, the identity function x, and such that whenever f and g are in the set, f+g, fg and f^g are also in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz (1984) computed the order type of the fragment below 2^(2^x). They did so by studying the possible limits at infinity of the quotient f(x)/g(x) of two functions in the fragment: if g is kept fixed and f varies, the possible limits form a discrete set of real numbers of order type omega. Using the surreal numbers, we extend the latter result to the whole class of Skolem functions and we discuss some additional progress towards the conjecture of Skolem. This is joint work with Marcello Mamino ( http://arxiv.org/abs/1911.07576 , to appear in the JSL).
Information: Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 9 April, 10:30am to 12:00pm Toronto time (16:30-18:00 CET)
Speaker: Joerg Brendle
Title: Combinatorics of ultrafilters on complete Boolean algebras 
Abstract: The combinatorial structure of ultrafilters on the natural numbers has been investigated intensively for many decades, and a lot is known about the order structure of such ultrafilters (under either the Tukey or the Rudin-Keisler ordering), about special classes of ultrafilters (like P-points),or about cardinal invariants related to ultrafilters (like the ultrafilter number). Yet, very little has beendone so far concerning combinatorial aspects of ultrafilters on general Boolean algebras, and thepurpose of this talk will be to present some basic results in this direction.
Focus will be put on the Tukey ordering, on (non)existence of non-Tukey-maximal ultrafilters, on ultrafilter numbers, and on an analogue of the Rudin-Keisler ordering in the context of complete Boolean algebras. We will in particular deal with Cohen and random algebras. This is joint work with Francesco Parente.
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 9 April, 2pm New York time (20:00 CET)
Speaker: Sandra Müller, University of Vienna
Title: The exact consistency strength of ‘AD + all sets are universally Baire’
Abstract: The large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is known to be much stronger than the Axiom of Determinacy itself. In fact, Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson showed that this would be optimal via a generalization of Woodin’s derived model construction. We will discuss a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and use this to prove Sargsyan’s conjecture.
Information: Please check on the seminar webpage if the seminar will take place. The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 29 March-4 April

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Caltech Logic Seminar
Time: Monday, 29 March, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Natasha Dobrinen, University of Denver
Title: Fraïssé classes with simply characterized big Ramsey degrees
Abstract: Analogues of the infinite Ramsey Theorem to infinite structures have been studied since the 1930s, when Sierpiński gave a coloring of pairs of rationals into two colors such that, in any subset of the rationals forming a dense linear order, both colors persist. In the 1970s Galvin showed that two is the optimum number for pairs of rationals, while Erdős, Hajnal and Pósa extended Sierpiński’s result to colorings of edges in the Rado graph. The next several decades saw a steady advance of results for other structures, a pinnacle of which was the 2006 work of Laflamme, Sauer, and Vuksanović, characterizing the exact number of colors for unavoidable colorings of finite graphs inside the Rado graph, and for similar Fraïssé structures with finitely many binary relations, including the generic tournament. This exact number is called the “big Ramsey degree”, a term coined by Kechris, Pestov, and Todorčević.
In this talk, we will provide a brief overview of the area of big Ramsey degrees infinite structures. Then we will present recent joint work with Coulson and Patel, showing that free amalgamation classes, in which any forbidden substructures are 3-irreducible, have big Ramsey degrees which are simply characterized. These results extend to certain strong amalgamation classes as well, extending the results of Laflamme, Sauer, and Vuksanović. This is in contrast to the more complex characterization of big Ramsey degrees for binary relational free amalgamation classes with forbidden 2-irreducible substructures, obtained in joint work of the speaker with Balko, Chodounský, Hubička, Konečný, Vena, and Zucker. The work with Coulson and Patel develops coding trees of quantifier-free 1-types and uses forcing to do an unbounded search for monochromatic finite objects. Furthermore, we work with skew subtrees with branching degree two which still code the Fraïssé limit. This allows for more ease when working with relations of arity greater than two, and also allows us to give the first proof of exact big Ramsey degrees bypassing the standard method of “envelopes”. It also sets the stage for current work of the speaker on infinite-dimensional Ramsey theory, in the vein of Galvin-Příkrý, for Fraïssé limits of free amalgamation classes in which any forbidden substructures are 3-irreducible.
Information: See the seminar webpage.

Münster research seminar on set theory
Time: Wednesday, 31 March, 15:15-16:45 CET
Speaker: tba
Title: tba
Abstract: tba
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 31 March, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Toronto Set Theory Seminar
Time: Friday, 2 April, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: tba
Title: tba
Abstract: tba
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 2 April, 2pm New York time (20:00 CET)
Speaker: Monroe Eskew, University of Vienna
Title: The approximation property and generic embeddings
Abstract: The approximation property was introduced by Hamkins for his Gap Forcing Theorem, and it has turned out to be a very useful notion, appearing for example in the partial equiconsistency result of Viale and Weiss on PFA, and in the proof of Woodin’s HOD Dichotomy Theorem. In the context of generic embeddings, there can be a useful interplay between elementarity and approximation. We discuss some recent work in this direction: (1) tensions between saturated ideals on ω2 and the tree property (with Sean Cox), (2) fragility of the strong independence spectra (with Vera Fischer), and (3) mutual inconsistency of Foreman‘s minimal generic hugeness axioms.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 22-28 March

For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 24 March, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Omer Ben-Neria
Title: The strong Prikry Property for Magidor iterations
Abstract: In his celebrated work on the identity crisis of strongly compact cardinals, Magidor introduced a special iteration of Prikry forcings for a set of measurable cardinals, known as the Magidor iteration. 
The purpose of this talk is to state and prove a version of the strong Prikry Lemma for such iterations, extending a result of Fuchs for the case where the set of measurables is discrete.  We will also describe several applications regarding the genericity of sequences of critical points in iterated ultrapowers.
Information: Please check on the seminar webpage if the seminar will take place. Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 24 March, 15:15-16:45 CET
Speaker: tba
Title: tba
Abstract: tba
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Paris-Lyon Séminaire de Logique
Time: Wednesday, 24 March, 16:00-17:00 CET
Speaker: Laura Fontanella, Paris
Title: Realizability and the Axiom of Choice
Abstract: Realizability aims at extracting the computational content of mathematical proofs. Introduced in 1945 by Kleene as part of a broader program in constructive mathematics, realizability has later evolved to include classical logic and even set theory. Krivine’s work led to define realizability models for the theory ZF following a general technique that generalizes the method of Forcing. However realizing the full Axiom of Choice is quite problematic. After a brief presentation of Krivine’s techniques, we will discuss the major obstacles for realizing the Axiom of Choice and I will present my recent joint work with Guillaume Geoffroy that led to realize weak versions of the Axiom of Choice for arbitrarily large cardinals.
Information: Join via the link on the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 24 March, 16:00-17:30 CET
Speaker: Peter Koellner, Harvard University
Title: Minimal models and $\beta$-categoricity
Abstract: Let us say that a theory T in the language of set theory is β-consistent at
α if there is a transitive model of T of height α, and let us say that it is
β-categorical at α iff there is at most one transitive model of T of height α.
The sentence V = L has the feature that ZFC + V = L is β-categorical at
α, for every α. If we assume in addition that ZFC + V = L is β-consistent at
α, then the uniquely determined model is Lα, and the minimal such model,
Lα0, is model of determined by the β-categorical theory ZFC + V = L + M,
where M is the statement “There does not exist a transitive model of ZFC.”
It is natural to ask whether V = L is the only sentence that can be β-
categorical at a countable ordinal α; that is, whether there can be a sentence φ such that for some countable α, ZFC + φ is β-categorical and β-consistent
at α, where the unique transitive model of height α is not Lα.
In the early 1970s Harvey Friedman proved a partial result in this direc-
tion. For a given ordinal α, let n(α) be the next admissible ordinal above α, and, for the purposes of this discussion, let us say that an ordinal α is
minimal iff a bounded subset of α appears in Ln(α) r Lα. [Note that α0 is
minimal (indeed a new subset of ω appears as soon as possible, namely, in
a Σ1-definable manner over Lα0+1) and an ordinal α is non-minimal iff Ln(α)
satisfies that α is a cardinal.] Friedman showed that for all countable α which
are non-minimal, V = L is the only sentence that is β-categorical at α. The
question of whether this is also true for α which are minimal has remained
open.
In this talk I will describe some joint work with Hugh Woodin that bears
on this question. In general, when approaching a “lightface” question (such as the one under consideration) it is easier to first address the “boldface”
analogue of the question by shifting from the context of L to the context
of L[x], where x is a real. In this new setting everything is relativized to
the real x: For an ordinal α, we let nx(α) be the first x-admissible ordinal
above α, and we say that α is x-minimal iff a bounded subset of α appears
in Lnx(α)[x] r Lα[x].
Theorem. Assume that there is an inner model with a Woodin cardinal and
that for all X, X# exists. There is a sentence φ in the language of set theory
with two additional constants, ̊c and ̊d, such that for a Turing cone of x,
interpreting ̊c by x, for all countable α,
(1) if Lα[x] |= ZFC, then there is an interpretation of ̊d by something in
Lα[x] such that there is a β-model of ZFC + φ of height α, and any
such model is not equal to Lα[x], and
(2) if, in addition, α is x-minimal, then there is a unique β-model of ZFC+φ
of height α, and this model is not equal to Lα[x].
The sentence φ asserts the existence of an object which is external to
Lα[x] and which, in the case where α is minimal, is canonical. The object
is a branch b through a certain tree in Lα[x], and the construction uses
techniques from the HOD analysis of models of determinacy.
In this talk I will sketch the proof, describe some additional features of
the singleton, and say a few words about why the lightface version looks
difficult.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

KGRC Research Seminar, Vienna
Time: Thursday, 25 March, 15:00-16:30 CET
Speaker: Iván Ongay-Valverde, University of Wisconsin–Madison, USA
Title: Splitting Localization and prediction numbers
Abstract: In 1993, Newelski and Roslanowski studied some cardinal characteristics related to the unsymmetric game (I, as Geschke, called them the localization numbers). While doing this, they found the n-localization property. When a forcing has this property, you can ensure that all new reals are ‘tame’ somehow (for example, you do not add Cohen or Random reals).
In a different line of study, Andreas Blass worked with some cardinal characteristics related to the idea of guessing correctly a real number given certain amount of information (he called them evasion and prediction numbers). In 2010, it was an open question whether some possible variations of these numbers were known cardinal characteristics or not.
Impressively, these two notions are related.
In this talk, we will show that the k global adaptive prediction numbers are not any other cardinal characteristic. In particular, they are not the localization numbers. To do this, we will use techniques analogue to Newelski and Roslanowski and we will show that the n-localization can be weakened to get their result.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 26 March, 16:30-18:30 CET
Speaker: Vincenzo Dimonte, University of Udine
Title: tba
Abstract: tba
Information: Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 26 March, 10.30-12pm Toronto time (15:30-17:00 CET)
Speaker: Sakaé Fuchino
Title: Laver-generically large cardinal and the Continuum Problem
Abstract: Let us call a class $\calP$ of posets iterable, if, for any $\poP\in\calP$ and $\calP$-name
$\utpoQ$\vspace{-0.5\smallskipamount} \st\ $\forces{\poP}{\utpoQ\in\calP}$, we have
$\poP\ast\utpoQ\in\calP$. 
For an iterable class $\mathcal{P}$ of posets, a cardinal $\mu$ is called {\it Laver-generically 
supercompact for $\mathcal{P}$}, if, for any $\mathbb{P}\in\mathcal{P}$ and $\lambda\in\On$,
there is a $\poP$-name $\utpoQ$\vspace{-0.5\smallskipamount} with $\forces{\poP}{\utpoQ\in\calP}$ \st, letting
$\poQ=\poP\ast\utpoQ$, 
there are $j$, $M\subseteq\uniV[\genH]$ for $(\uniV, \mathbb{Q})$-generic 
$\genH$ such that
1) $\elembed{j}{V}{M}$,\smallskip
2) $crit(j)=\mu$, $j(\mu)>\lambda$,\smallskip
3) $\cardof{\poQ}\leq j(\mu)$,\smallskip
4) $\poP$, $\genH\in M$ and \smallskip
5) $j\imageof\lambda\in M$.\\\\
The notion of Laver-generically superhugeness is obtained when \assert{5} is replaced by
5′) $j\imageof j(\mu)\in M$. 
The notion of Laver-generically large cardinal for $\calP$ given here is stronger than the one introduced in \cite{II} and is called there the {\it strongly} and {\it tightly} 
Laver-generically large cardinal (the strongness corresponds the usage of two-step 
iteration in the definition instead of just $\poP\circleq\poQ$, and the tightness the 
condition \assert{3}).
In my talk, I will give a proof of the following:\quad
For many natural iterable class of proper posets $\mathcal{P}$, a 
Laver-generically supercompact cardinal $\mu$ for $\poP$ is either $\aleph_2$ or very large (if it exists),  and the continuum is either $\aleph_1$ or $\aleph_2$, or $\geq\mu$ in case of very large $\mu$, where it depends on $P$ which scenario we have. 
If time allows, I will also sketch a proof of the following theorem:\quad
If $\mathcal{P}$ is the class of c.c.c.\ posets (or some other iterable class $\calP$ of posets preserving all  cardinalities but adding some real), and if $\mu$ is Laver-generically superhuge for $\mathcal{P}$, then $\mu=2^{\aleph_0}$. 
At the moment, it is open if the same theorem holds for a Laver-generically supercompact.
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 26 March, 11am New York time (16:00 CET)
Speaker: Carolin Antos, University of Konstanz
Title: The ‘algebraic’ vs. ‘non-algebraic’ distinction: New impulses for the universe/multiverse debate?
Abstract: The distinction between ‘algebraic’ and ‘non-algebraic fields in mathematics, coined by Shapiro (1997), plays an important role in discussions about the status of set theory and connects back to the so-called universe/multiverse debate in the philosophy of set theory. In this talk we will see, that this distinction is not as clear cut as is usually assume when using it in the debate. In particular, we will see that in more recent formulations of this distinction, multiversism seems to split into a a strong and a weaker form. This can be translated to a meta-level, when considering the background theory in which set-theoretic multiversism can take place. This offers a more fine-grained picture of multiversism and allows us to mitigate a standard universist objection based on the conception of a multiversist background theory.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 15-21 March

Caltech Logic Seminar
Time: Monday, 15 March, 12:00 – 1:00pm Pacific time (20:00 CET)
Speaker: Vladimir Kanovei, IITP, Moscow
Title: An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited
Abstract: A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and E0-large generic extensions of the constructible universe LL. More specifically, if aa is a real either Sacks generic or E0 generic over L, then it is true in L[a] that: there is a Π21 equivalence relation Q on the set U, of all nonconstructible reals, with exactly two equivalence classes, and both those classes are non-OD sets. This is joint work with Ali Enayat.
Information: See the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 17 March, 16:00-17:30 CET
Speaker: Wojciech Woloszyn, University of Oxford
Title: Modal graph theory as a foundation of mathematics
Abstract: One can consider the class of all graphs as a Kripke model of possible worlds, where a graph extends or accesses a larger graph just in case it is an induced subgraph thereof. In this way, we can introduce modal operators of possibility and necessity. A statement is possible at a graph if it is true in some extension of that graph, and it is necessary if it is true at all such extensions. We can thus enlarge the first-order language of graphs by closing it under modal operators, Boolean connectives, and quantification. The resulting modal language of graph theory turns out to be rather fruitful—it can express finiteness, countability, size continuum, size א1, א2, אω, first ב fixed-point, first ב-hyper-fixed-point, and so on. Perhaps most remarkably, modal graph theory can interpret set-theoretic truth in Vθ for quite a long way into the
cumulative hierarchy. Does it run out of steam or can it interpret truth in the full set-theoretic universe V, and serve as a foundation of mathematics
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Münster research seminar on set theory
Time: Wednesday, 17 March, 15:15-16:45 CET
Speaker: tba
Title: tba
Abstract: tba
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Ghent-Leeds Virtual Logic Seminar
Time: Thursday, 18 March, 2pm UK time (15:00 CET)
Speaker: Aleksandra Kwiatkowska, University of Münster and University of Wrocław
Title: Simplicity of the automorphism groups of countable structures
Abstract: The program of understanding the normal subgroup structure of groups that arise as automorphism groups of countable structures dates back at least to the ’50s, when Higman described all proper normal subgroups of the automorphism group of rationals (Q,<).  In recent several years Tent-Ziegler, following the work of Macpherson-Tent, proved simplicity for many automorphism groups of countable graphs and metric spaces.  In the talk, we prove simplicity for the automorphism groups of order and tournament expansions of ultrahomogeneous structures like the bounded Urysohn metric space and the random graph.  In particular, we show that the automorphism group of the linearly ordered random graph is a simple group.  This is joint work with Filippo Calderoni and Katrin Tent.
Information: Please contact Paul Shafer in advance to participate.

KGRC Research Seminar, Vienna
Time: Thursday, 18 March, 15:00-16:30 CET
Speaker: Jaroslav Šupina, Pavol Jozef Šafárik University in Košice, Slovakia
Title: Partition forcing
Abstract: A. Miller introduced in 1980 a forcing notion we refer to as a partition forcing.  Although it is a variant of Sacks’ perfect set forcing, it is closely related to Miller’s rational perfect set forcing.
The talk is devoted to our application of partition forcing in a proof of consistency of u=i<aT. Here, i is the minimal cardinality of a maximal independent family, u a minimal size of an ultrafilter base, and aT is the minimal cardinality of a maximal family of pairwise almost disjoint subtrees of 2<ω.
This is a joint work with Vera Fischer.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 19 March, 16:30-18:30 CET
Speaker: G. Paolini, Turin
Title: Torsion-Free Abelian Groups are Borel Complete
Abstract: We prove that the Borel space of torsion-free Abelian groups with domain \omega is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a long-standing open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and Stanley from 1989.
Information: Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 19 March, 1.30-3pm Toronto time (18:30-20:00 CET)
Speaker: Anush Tserunyan
Title: Ergodic theorems along trees
Abstract: In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation $T$, one takes averages of a given integrable function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in the forward orbit of the point $x$. In joint work with Jenna Zomback, we prove a “backward” ergodic theorem for a countable-to-one pmp $T$, where the averages are taken over subtrees of the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Surprisingly, this theorem yields (forward) ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank where the averages are taken along subtrees of the standard Cayley graph rooted at the identity. For free group actions, this strengthens the best known result in this vein due to Bufetov (2000).
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 19 March, 2pm New York time (19:00 CET)
Speaker: Paul Blain Levy, University of Birmingham
Title: Broad Infinity and Generation Principles
Abstract: Broad Infinity is a new and arguably intuitive axiom scheme in set theory. It states that ‘broad numbers’, which are three-dimensional trees whose growth is controlled, form a set. If the Axiom of Choice is assumed, then Broad Infinity is equivalent to the Ord-is-Mahlo scheme: every closed unbounded class of ordinals contains a regular ordinal.
Whereas the axiom of Infinity leads to generation principles for sets and families and ordinals, Broad Infinity leads to more advanced versions of these principles. The talk explains these principles and how they are related under various prior assumptions: the Axiom of Choice, the Law of Excluded Middle, and weaker assumptions.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online Activities 8-14 March

Caltech Logic Seminar
Time: Monday, 8 March, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Maciej Malicki, IMPAN
Title: Infinitary continuous logic and descriptive set theory
Abstract: There are deep connections between model theory of the infinitary logic Lω1ωLω1ω and descriptive set theory: Scott analysis, the López-Escobar theorem or the Suzuki theorem are well known examples of this phenomenon. In this talk, I would like to present results of an ongoing research devoted to generalizing these connections to the setting of continuous infinitary logic and Polish metric structures. In particular, I will discuss a continuous counterpart of a theorem of Hjorth and Kechris characterizing essential countability of the isomorphism relation on a given Borel class of countable structures. As an application, I will give a short model-theoretic proof of a result of Kechris saying that orbit equivalence relations induced by continuous actions of locally compact Polish groups are essentially countable. This is joint work with Andreas Hallbäck and Todor Tsankov.
Information: See the seminar webpage.

Caltech Logic Seminar
Time: Monday, 8 March, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Maciej Malicki, IMPAN
Title: Infinitary continuous logic and descriptive set theory
Abstract: There are deep connections between model theory of the infinitary logic Lω1ωLω1ω and descriptive set theory: Scott analysis, the López-Escobar theorem or the Suzuki theorem are well known examples of this phenomenon. In this talk, I would like to present results of an ongoing research devoted to generalizing these connections to the setting of continuous infinitary logic and Polish metric structures. In particular, I will discuss a continuous counterpart of a theorem of Hjorth and Kechris characterizing essential countability of the isomorphism relation on a given Borel class of countable structures. As an application, I will give a short model-theoretic proof of a result of Kechris saying that orbit equivalence relations induced by continuous actions of locally compact Polish groups are essentially countable. This is joint work with Andreas Hallbäck and Todor Tsankov.
Information: See the seminar webpage.

Singapore Logic Seminar
Time: Wednesday, 10 March, 17:00-18:00 Singapore time (10:00-11:00 CET)
Speaker: Zekun Jia
Title: Two Ramsey-theoretic statements in models where AC fails
Abstract: There are a lot of theorems in Ramsey theory whose proof explicitly or implicitly uses the Axiom of Choice. This talk will focus on Ramsey’s Theorem and Open Ramsey Theorem in three models of set theory where the Axiom of Choice fails (the basic Cohen model, the basic Fraenkel model, and the ordered Mostowski model), as well as some consistency and independence results that follow. Also, the usual proof of Open Ramsey Theorem on omega given by Galvin and Prikry assumes the Axiom of Dependent Choice, and this talk will sketch an improvement on that proof to make it purely constructive. This talk is about a project advised by Zach Norwood. 
Information: See the seminar webpage.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 10 March, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Yair Hayut 
Title: Stationary reflection and Prikry forcing – Part II
Abstract: In 1982, Magidor proved the consistency of stationary reflection at \aleph_{\omega+1}, relative to an \omega-sequence of supercompact cardinals. Square based heuristics indicated that a much weaker large cardinal hypothesis is the correct strength. In a sequence of results of various authors, Magidor’s result was gradually improved to stationary reflection at all sets except one “bad” stationary set at \aleph_{\omega+1}, starting with a large cardinal property weaker than \kappa^+-supercompactness. In a joint work with Unger, we managed to obtain the consistency of (full) stationary reflection, from what seems to be close to the optimal hypothesis.In this talk I will present the main ideas behind the proof (which is the interplay between Prikry type forcings and iterated ultrapowers). This method shares some features with the Sigma-Prikry framework, where the main difference is its non-iterative nature.In a joint work with Ben-Neria, we tackled the problem of combining the failure of SCH with stationary reflection, starting with a similar large cardinal hypothesis. In order to do that, we used a similar analysis of the extender based Prikry forcing. 
Information: Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

Münster research seminar on set theory
Time: Wednesday, 10 March, 15:15-16:45 CET
Speaker: tba
Title: tba
Abstract: tba
Information: Please check the seminar webpage to see if the seminar takes place. Contact rds@wwu.de ahead of time in order to participate.

Paris-Lyon Séminaire de Logique
Time: Wednesday, 10 March, 16:00-17:00 CET
Speaker: Zoltán Vidnyánszky
Title: Bases for Borel graphs of large chromatic number
Abstract: The first part of my talk will be an introduction to the field of Borel combinatorics. I will survey some of the most important results and discuss the connections to other fields. In the second part, I will talk about the structure of the collection of graphs with large Borel chromatic number, and whether it is possible to simply characterize them.
Information: Join via the link on the seminar webpage.

Barcelona Set Theory Seminar
Time: Wednesday, 10 March, 16:00-17:30 CET
Speaker: Carolin Antos, University of Konstanz
Title: The “algebraic” vs. “non-algebraic” distinction: New impulses for the universe/multiverse debate?
Abstract: The distinction between “algebraic” and “non-algebraic” fields in mathematics, coined by Shapiro (1997), plays an important role in discussions about the status of set theory and connects back to the so-called universe/multiverse debate in the philosophy of set theory. In this talk we will see that this distinction is not as clear cut as is usually assumed when using it in the debate. In particular, we will see that in more recent formulations of this distinction, multiversism seems to split into a strong and a weaker form. This can be translated to a meta-level, when considering the background theory in which set-theoretic multiversism can take place. This offers a more fine-grained picture of multiversism and allows us to mitigate a standard universist objection based on the conception of a multiversist background theory.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.

Bristol Logic and Set Theory Seminar/Oxford Set Theory Seminar
Time: Wednesday, 10 March, 16:00-17:30 UK time (17:00-18:30 CEST)
Speaker: Peter Koellner, Harvard University
Title: Minimal Models and β-Categoricity
Abstract: Let us say that a theory T in the language of set theory is β-consistent at α if there is a transitive model of T of height α, and let us say that it is β-categorical at α iff there is at most one transitive model of T of height α. Let us also assume, for ease of formulation, that there are arbitrarily large α such that ZFC is β-consistent at α.
The sentence V = L has the feature that ZFC + V = L is β-categorical at α, for every α. If we assume in addition that ZFC + V = L is β-consistent at α, then the uniquely determined model is Lα, and the minimal such model, Lα0 , is model of determined by the β-categorical theory ZFC + V = L + M, where M is the statement “There does not exist a transitive model of ZFC.”
It is natural to ask whether V=L is the only sentence that can be β- categorical at α; that is, whether, there can be a sentence φ such that ZFC+φ is β-categorical at α, β-consistent at α, and where the unique model is not Lα. In the early 1970s Harvey Friedman proved a partial result in this direction. For a given ordinal α, let n(α) be the next admissible ordinal above α, and, for the purposes of this discussion, let us say that an ordinal α is minimal iff a bounded subset of α appears in Ln(α) Lα. [Note that α0 is minimal (indeed a new subset of ω appears as soon as possible, namely, in a Σ_1-definable manner over L(α0+1) and an ordinal α is non-minimal iff Ln(α) satisfies that α is a cardinal.] Friedman showed that for all α which are non-minimal, V = L is the only sentence that is β-categorical at α. The question of whether this is also true for α which are minimal has remained open.
In this talk I will describe some joint work with Hugh Woodin that bears on this question. In general, when approaching a “lightface” question (such
1
as the one under consideration) it is easier to first address the “boldface” analogue of the question by shifting from the context of L to the context of L[x], where x is a real. In this new setting everything is relativized to the real x: For an ordinal α, we let nx(α) be the first x-admissible ordinal above α, and we say that α is x-minimal iff a bounded subset of α appears in Lnx(α)[x] \ Lα[x].
Theorem. Assume M1# exists and is fully iterable. There is a sentence φ in the language of set theory with two additional constants, ̊c and ̊d, such that for a Turing cone of x, interpreting ̊c by x, for all α
(1) if Lα[x] |= ZFC then there is an interpretation of ̊d by something in Lα[x] such that there is a β-model of ZFC+φ of height α and not equal to Lα[x], and
(2) if, in addition, α is x-minimal, then there is a unique β-model of ZFC+φ of height α and not equal to Lα[x].
The sentence φ asserts the existence of an object which is external to Lα[x] and which, in the case where α is minimal, is canonical. The object is a branch b through a certain tree in Lα[x], and the construction uses techniques from the HOD analysis of models of determinacy.
In this talk I will sketch the proof, describe some additional features of the singleton, and say a few words about why the lightface version looks difficult.
Information: For the Zoom access code, contact Samuel Adam-Day me@samadamday.com. Link: https://zoom.us/j/96803195711 (open 30 minutes before)

KGRC Research Seminar, Vienna
Time: Thursday, 11 March, 15:00-16:30 CET
Speaker: Sandra Müller, TU Wien and Universität Wien
Title: The exact consistency strength of “AD+ + all sets are universally Baire”
Abstract: The large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is known to be much stronger than the Axiom of Determinacy itself. In fact, Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson showed in 2014 that this would be optimal via a generalization of Woodin’s derived model construction. We will discuss a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and use this to prove Sargsyan’s conjecture.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 12 March, 16:30-18:30 CET
Speaker: Clinton Conley, Carnegie Mellon University
Title: Dividing the sphere by rotations
Abstract: We say that a subset A of the sphere r-divides it if r-many rotations of A perfectly tile the sphere’s surface. Such divisions were first exhibited by Robinson (47) and developed by Mycielski (55). We discuss a colorful approach to finding these divisions which are Lebesgue measurable or possess the property of Baire. This includes joint work with J. Grebik, A. Marks, O. Pikhurko, and S. Unger.
Information: Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 12 March, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: Menachem Kojman
Title: Strong colorings over partitions
Abstract: Strong colorings over partitions were introduced last year by Chen-Mertens, Kojman and Steprans. 
In the talk I will present the subject and continue to present the next step of the theory, which was developed in a recent  joint work by Kojman, Rinot and Steprans. 
The advances include stretching arguments which use Walks on Ordinals. I will present this new technique. 
Information: No webpage available. Email Ivan Ongay Valverde to receive the seminar announcements and for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 12 March, 2pm New York time (20:00 CET)
Speaker: Hossein Lamei Ramandi, Cornell University
Title: Galvin’s question on non-σ-well ordered linear orders
Abstract: Assume C is the class of all linear orders L such that L is not a countable union of well ordered sets, and every uncountable subset of L contains a copy of ω1. We show it is consistent that C has minimal elements. This answers an old question due to Galvin.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Kobe Set Theory Workshop 2021

Kobe Set Theory Workshop 2021— on the occasion of Sakaé Fuchino’s retirement —(Online Workshop via ZOOM)

Dates: March 9th (Tue.) — 11th (Thu.)

Webpage: http://www2.kobe-u.ac.jp/~hsakai/Fuchino2021/

Speakers: 
– Sakaé Fuchino (Kobe University) 
– Joan Bagaria (University of Barcelona) 
– Joel David Hamkins (Oxford University) 
– Paul Larson (Miami University) 
– David Aspero (University of East Anglia) 
– Piotr Borodulin-Nadzieja (University of Wrocław) 
– Andrew Brooke-Taylor (University of Leeds) 
– Chris Lambie-Hanson (Virginia Commonwealth University) 
– Teruyuki Yorioka (Shizuoka University) 
– Toshinmichi Usuba (Waseda University) 
– Daisuke Ikegami (Shibaura Institute of Technology) 
– Diego Mejia (Shizuoka University)

Registration: Only registered participants will have access to the ZOOM Meeting link.
For the registration, please click the following link. https://kobe-u-ac-jp.zoom.us/meeting/register/tZYqde2oqjstH9QW5CXr6eWuUM3oMdbQ7xFE

After the registration, organizers will approve it within a day. Then, you will receive the ZOOM Meeting link by e-mail.

If you have any questions, please contact Hiroshi Sakai by e-mail.

Contact: hsakai@people.kobe-u.ac.jp

Online Activities 1-7 March

Caltech Logic Seminar
Time: Monday, 1 March, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Filippo Calderoni, University of Illinois at Chicago
Title: Anticlassification results for groups acting freely on the line
Abstract: In this talk we shall discuss some anticlassification results for orderable groups. First, we introduce the space of Archimedean orderings Ar(G)Ar⁡(G) for a given countable orderable group GG. We prove that the equivalence relation induced by the natural action of GL2(Q)GL2⁡(Q) on Ar(Q2)Ar⁡(Q2) is not concretely classifiable. Then we shall discuss the complexity of the isomorphism relation for countable ordered Archimedean groups. In particular, we show that its potential class is not Π03Π30. This topological constraint prevents classifying ordered Archimedean groups using countable subsets of reals. Our proofs combine classical results on Archimedean groups, the theory of Borel equivalence relations, and analyzing definable sets in the basic Cohen model and other models of Zermelo-Fraenkel set theory without choice. This is joint work with Dave Marker, Luca Motto Ros, and Assaf Shani.
Information: See the seminar webpage.

Singapore Logic Seminar
Time: Wednesday, 3 March, 17:00-18:00 Singapore time (10:00-11:00 CET)
Speaker: Desmond Lau
Title: On the unification of two “maximal” axioms
Abstract: Martin’s Maximum^{++} and Woodin’s axiom (*) are two statements independent of, but consistent with, ZFC. I will present the common reasons they are appealing as set-theoretic axioms, before comparing the sense in which they are “maximal”. I will also run through an exposition of the recent work by Aspero and Schindler, which shows Martin’s Maximum^{++} implies (*), effectively “unifying” the statements.
Information: See the seminar webpage.

MOPA (Models of Peano Arithmetic), CUNY
Time: Wednesday, 3 March, 7pm New York time (01:00 CET on 4 March)
Speaker: Ali Enayat, University of Gothenburg
Title: PA with a class of indiscernibles
Abstract: This talk focuses on the theory PAI (I for Indiscernibles), a theory formulated in the language of PA augmented with a unary predicate I(x). Models of PAI are of the form (M,I) where (1) M is a model of PA, (2) I is a proper class of M, i.e., I is unbounded in M and (M,I) satisfies PA*, and (3) I forms a class of indiscernibles over M. The formalizability of the Infinite Ramsey Theorem in PA makes it clear that PAI is a conservative extension of PA. As we will see, nonstandard models of PA (of any cardinality) that have an expansion to a model of PAI are precisely those nonstandard models PA that can carry an inductive partial satisfaction class. The formulation and investigation of PAI was inspired by my work on the set theoretical sibling ZFI of PAI, whose behavior I will also compare and contrast with that of PAI.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Hebrew University-Bar Ilan University Set Theory seminar
Time: Wednesday, 3 March, 14:00-16:00 Israel Time (13:00-15:00 CET)
Speaker: Yair Hayut 
Title: Stationary reflection and Prikry forcing
Abstract: In 1982, Magidor proved the consistency of stationary reflection at \aleph_{\omega+1}, relative to an \omega-sequence of supercompact cardinals. Square based heuristics indicated that a much weaker large cardinal hypothesis is the correct strength. In a sequence of results of various authors, Magidor’s result was gradually improved to stationary reflection at all sets except one “bad” stationary set at \aleph_{\omega+1}, starting with a large cardinal property weaker than \kappa^+-supercompactness. In a joint work with Unger, we managed to obtain the consistency of (full) stationary reflection, from what seems to be close to the optimal hypothesis.In this talk I will present the main ideas behind the proof (which is the interplay between Prikry type forcings and iterated ultrapowers). This method shares some features with the Sigma-Prikry framework, where the main difference is its non-iterative nature.In a joint work with Ben-Neria, we tackled the problem of combining the failure of SCH with stationary reflection, starting with a similar large cardinal hypothesis. In order to do that, we used a similar analysis of the extender based Prikry forcing. 
Information: Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

KGRC Research Seminar, Vienna
Time: Thursday, 4 March, 15:00-16:30 CET
Speaker: Allen Gehret, University of Vienna
Title: Asymptotic differential algebra and logarithmic transseries
Abstract: In this talk I will give a brief introduction to the subject ‘Asymptotic Differential Algebra’ and an overview of the logarithmic transseries programme. The intuition originates in freshman calculus (specifically: limits, l’hopital’s rule, convergence/divergence of integrals and series, asymptotic expansions). The mathematical concepts primarily involve various flavors of fields (equipped with a derivation and/or a valuation and/or an ordering). The logical content will be minimal: first-order languages, model completeness, quantifier elimination.
Information: Talk via zoom.

Turin-Udine logic seminar
Time: Friday, 5 March, 16:30-18:30 CET
Speaker: Noe de Rancourt, University of Vienna
Title: A dichotomy for countable unions of smooth Borel equivalence relations
Abstract: I will present a dichotomy for equivalence relations on Polish spaces that can be expressed as countable unions of smooth Borel equivalence relations. It can be seen as an extension of Kechris-Louveau’s dichotomy for hypersmooth Borel equivalence relations. A generalization of our dichotomy, for equivalence relations that can be expressed as countable unions of Borel equivalence relations belonging to certain fixed classes, will also be presented. This is a joint work with Benjamin Miller.
Information: Online on WebEx. Please see the seminar webpage.

Toronto Set Theory Seminar
Time: Friday, 5 March, 1.30-3pm Toronto time (19:30-21:00 CET)
Speaker: Alan Dow
Title: On the cardinality of separable pseudoradial spaces
Abstract: A point is in the radial closure of a set A if there is a well-ordered sequence from A converging to the point. A set is radially closed if all points in the radial closure are in the set.  A space is radial if the radial closure of a set equals its closure and is pseudoradial if every radially closed set is closed.
 One can observe that the notions of Frechet-Urysohn and sequential are the related notions when restricted to the usual countable sequences. Motivatedby some work and questions by Santi Spadaro,  Istvan Juhasz asked about  the implicit question raised by the title.  We discuss our progress on the problem in joint work with Istvan Juhasz.
Information: Email Ivan Ongay Valverde ahead of time for the zoom link.

CUNY Set Theory Seminar
Time: Friday, 5 March 26, 2pm New York time (20:00 CET)
Speaker: Hiroshi Sakai, Kobe University
Title: Generalized stationary reflection and cardinal arithmetic
Abstract: The stationary reflection principle, which is often called the Weak Reflection Principle, is known to have many interesting consequences. As for cardinal arithmetic, it implies that λω=λ for all regular cardinal λ≥ω2. In this talk, we will discuss higher analogues of this stationary reflection principle and their consequences on cardinal arithmetic.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.