The announcements are updated continuously. For a list of talks in the coming weeks, please see here.
Kobe Set Theory Seminar
Time: Monday, 15 May, 16:30 local time (09:30 CEST)
Speaker: Takehiko Gappo, TU Wien
Title: Chang models over derived models with supercompact measures (1/2)
Abstract: The relationship between the Axiom of Determinacy and supercompactness of ω1 has been studied by many people. In 1990’s, Woodin showed that assuming the existence of a proper class of Woodin limits of Woodin cardinals, a generalized Chang model satisfies “ADℝ + ω1 is supercompact.” Recently he also showed that the regularity of Θ in the model follows from determinacy of a long game of length ω1, which is, however, still unknown to be consistent. Based on these results, we conjecture that the following two theories are equiconsistent:
(1) ZFC + there is a Woodin limit of Woodin cardinals.
(2) ZF + ADℝ + Θ is regular + ω1 is supercompact.
Toward this conjecture, we construct a new model of the Axiom of Determinacy, called the Chang model over the derived model with supercompact measures. We then prove that it is consistent relative to a Woodin limit of Woodin cardinals that our model satisfies “ADℝ + Θ is regular + ω1 is < δ-supercompact for some regular cardinal δ > Θ.” This is joint work with Sandra Müller and Grigor Sargsyan.
Information: Please see the seminar webpage. This talk will be given in hybrid format. Please email Hiroshi Sakai for the zoom information in advance.
Baltic Set Theory Seminar
Time: Tuesday, 16 May, 15:00-16:30 CEST
Speaker: Several
Title: Baltic Set Theory Seminar
Abstract: This is a learning seminar, the goal is to actually go over proofs and more or less understand them. Discussions are encouraged. The topic of the seminar is the following:
1. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.
2. Paul Larson, A course on AD^+
Information: Please see the seminar webpage.
Leeds Models and Sets Seminar
Time: Wednesday, 17 May, 13:45-15:00 local time (14:45-16:00 CEST)
Speaker: Will Boney, Texas State University
Title: Building generalized indiscernibles in nonelementary classes
Abstract: Generalized indiscernibles can be built in first-order theories by generalizing the combinatorial Ramsey’s Theorem to classes with more structure, which is an active area of study. Trying to do the same for infinitely theories (in the guise of Abstract Elementary Classes) requires generalizing the Erdos-Rado Theorem instead. We discuss various results about generalizations of the Erdos-Rado Theorem and techniques (including large cardinals and forcing) to build generalized indiscernibles.
Information: Please see the seminar webpage.
Caltech Logic Seminar
Time: Wednesday, 17 May, 12:00am-13:00pm Pacific time (21:00-22:00 CEST)
Speaker: Forte Shinko, UCLA
Title: The generic action of a free group on Cantor space is hyperfinite
Abstract: Let Γ be a countable free group. The set of continuous actions of Γ on Cantor space 2N admits a natural Polish topology, and hence we can talk about properties of the generic action. It was shown by Frisch-Kechris-Shinko-Vidnyánszky that the generic action is measure-hyperfinite, meaning that for every Borel probability measure μ on 2N, the action is hyperfinite modulo some μ-null set. Kwiatkowska showed using the methods of projective Fraïssé theory that there is only one generic action up to isomorphism. We use her techniques to investigate the generic action further, and in particular we show that the generic action is hyperfinite. This is joint work with Sumun Iyer.
Information: Please see the seminar webpage.
Renyi Institute Set Theory Seminar
Time: Thursday, 18 May, 10:30 – 12:00 CEST
Speaker: Amitayu Banerjee
Title: On a variant of Erdős–Dushnik–Miller theorem without the Axiom of Choice (AC)
Abstract: Theories: ZFC (Zermelo–Fraenkel set theory with the Axiom of Choice (AC)), ZF (Zermelo–Fraenkel set theory without AC), ZFA (ZF with the Axiom of Extensionality weakened to allow the existence of atoms).
Known informations:
In 1941, Ben Dushnik and Miller established the proposition “Every infinite graph contains either a countably infinite independent set or a clique with the same cardinality as the whole graph” in ZFC, and gave credit to Paul Erdős for the proof of the result for the case in which the cardinality of the graph is a singular cardinal. The above result is uniformly known as Erdős–Dushnik–Miller theorem.
Consider the following variant (abbreviated as EDM): “Every uncountable graph contains either a countably infinite independent set or an uncountable clique”. It is well-known that in ZFC, EDM implies the proposition “Any partially ordered set such that all of its antichains are finite and all of its chains are countable is countable” (we abbreviate by K) as well as the infinite Ramsey’s theorem (“Every infinite graph has either an infinite independent set or an infinite clique”).
In 1977, Andreas Blass studied the exact placement of the infinite Ramsey’s theorem in the hierarchy of weak forms of AC. In particular, he proved that the Boolean Prime Ideal Theorem (a weak form of AC) is independent of the infinite Ramsey’s theorem in ZF (i.e., there exists a ZF model where the Boolean Prime Ideal Theorem holds, but the infinite Ramsey’s theorem fails, and there exists a ZF model where the infinite Ramsey’s theorem holds, but the Boolean Prime Ideal Theorem fails) (see: https://doi.org/10.2307/2272866).
In 2021, I studied some relations of K with weak forms of AC. (see: arXiv:2009.05368v2; to appear).
In 2022, Eleftherios Tachtsis investigated the deductive strength of K without AC in more detail. Among several results, Tachtsis proved that DC_{\aleph_{1}} (Dependent Choices for \aleph_{1}, a weak form of AC stronger than Dependent Choices (DC)) implies K in ZF (see: https://link.springer.com/article/10.1007/s00605-022-01751-9).
New Results: We study the exact placement of EDM in the hierarchy of weak forms of AC. In particular, we prove the following results (see arXiv:2211.05665v3):
1. The strength of EDM is strictly between DC_{\aleph_{1}} and K in ZFA.
2. EDM is strictly stronger than the infinite Ramsey’s theorem in ZF (i.e., the infinite Ramsey’s theorem does not imply EDM in ZF).
3. The Boolean Prime Ideal Theorem is independent of EDM in ZFA (specifically, neither the Boolean Prime Ideal Theorem implies EDM in ZF, nor EDM implies the Boolean Prime Ideal Theorem in ZFA).
Finally, the speaker will state some open questions in this track.
Information: Please see the seminar webpage. This talk will be given in hybrid format.
Cross-Alps Logic Seminar
Time: Friday, 19 May, 16.00-17.00 CEST
Speaker: J. Duparc, Université de Lausanne
Title: tba
Abstract: tba
Information: The event will stream on the Webex platform. Please write to luca.mottoros [at] unito.it for the link to the event.
CUNY Set Theory Seminar
Time: Friday, 19 May, 12:30pm New York time (18:15 CEST)
Speaker: Miha Habič, Bard College at Simon’s Rock
Title: Some old and new results on nonamalgamable forcing extensions
Abstract: Fixing some countable transitive model M of set theory, we can consider its generic multiverse, the family of all models obtainable from M by taking any sequence of forcing extensions and ground models. There is an attractive similarity between the generic multiverse and the Turing degrees, but the multiverse has the drawback (or feature?) that it contains nonamalgamable models, that is, models with no common upper bound, as was observed by several people, going back to at least Mostowski. In joint work with Hamkins, Klausner, Verner, and Williams in 2019, we studied the order-theoretic properties of the generic multiverse and, among other results, gave a characterization of which partial orders embed nicely into the multiverse. I will present our results in the simplest case of Cohen forcing, as well as existing generalizations to wide forcing, and some new results on non-Cohen ccc forcings.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.
Toronto Set Theory Seminar
Time: Friday, 19 May, 1.30-3.00 Toronto time (19.30-21.00 CEST)
Speaker: Vera Fischer, University of Vienna
Title: tba
Abstract: tba
Information: Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.
European Set Theory Society 