The announcements are updated continuously. For a list of talks in the coming weeks, please see here.

**Baltic Set Theory Seminar****Time:** Tuesday, 2 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.

**Hebrew University-Bar Ilan University Set Theory seminar****Time:** Wednesday, 3 May, 13:00-15:00 Israel Time (12:00-14:00 CEST)**Speaker:** tba **Title:** tba **Abstract:** tba **Information:** Contact Menachem Magidor or Omer Ben-Neria ahead of time for the zoom link.

**Leeds Models and Sets Seminar****Time:** Wednesday, 3 May, 13:45-15:00 local time (14:45-16:00 CEST)**Speaker:** Vahagn Aslanyan, University of Leeds**Title:** Combining Manin-Mumford and weak Zilber-Pink**Abstract:** I will introduce some classical notions and problems in Diophantine geometry, including the Manin-Mumford and Zilber-Pink conjectures, and explain how model-theoretic tools are used to approach them. I will then talk about one of my recent theorems establishing a new partial result towards Zilber-Pink by combining Manin-Mumford and a weak version of Zilber-Pink (both are theorems). I am going to start with very basic things, give quite a few examples and define/explain all concepts that I am going to use, so I hope that most of the talk will be accessible to a wide range of people including those who have not heard about Diophantine geometry before.**Information:** Please see the seminar webpage.

**Caltech Logic Seminar****Time:** Wednesday, 3 May, 12:00am-13:00pm Pacific time (21:00-22:00 CEST)**Speaker:** Jan Grebík, University of Warwick**Title:** Measurable Vizing’s theorem**Abstract:** Vizing’s theorem asserts that every graph of degree bounded by Δ<+∞ admits a proper edge coloring with (Δ+1) colors. I will discuss versions of this theorem in the context of measurable graph combinatorics. I will mainly focus on the case when the graph in question is defined on a standard probability space (X,μ). In this situation, a combination of an augmenting chain technique developed earlier with Oleg Pikhurko (that was applied for graphings) together with a new result about quasi-invariant measures allows to deduce a full analogue of Vizing’s theorem.**Information:** Please see the seminar webpage.

**Renyi Institute Set Theory SeminarTime:** Thursday, 4 May, 10:30 – 12:00 CEST

**Speaker:**Lajos Soukup, Renyi Institute

**Title:**Minimal Vertex Covers in Infinite Hypergraphs

**Abstract:**A “vertex cover” of a hypergraph is a set of vertices which intersects each hyperedge. A hypergraph possesses “property

*C*(

*k*,

*ρ*)” iff |⋂E′|<

*ρ*for each

*k*element set E′ of hyperedges. Komjáth proved that every uniform hypergraph possessing property

*C*(2,

*r*) for some

*r*∈

*ω*has a minimal vertex cover. We could relax the assumption of uniformity to an assumption that the set of cardinalities of the hyperedges is a “small” set of infinite cardinals, e.g. it is countable, or it does not contain uncountably many limit cardinals. Komjáth also proved that GCH does not decide the following statement: “If a hypergraph

*G*possessing property

*C*(2,

*ω*) is

*μ*-uniform for some

*μ*≥

*ω*1, then

*G*has a minimal vertex cover.

Using Shelah’s Revised GCH theorem, we could show that if we strengthen the assumption

*μ*≥

*ω*1 to

*μ*≥

*bethω*, then we can prove the statement in ZFC! We also show that if all the hyperedges of a hypergraph are countably infinite, then instead of

*C*(2,

*r*) the assumption

*C*(

*k*,

*r*) (for some

*k*∈

*ω*) is enough to guarantee the existence of a minimal vertex cover. If every hyperedge has cardinality

*ω*1, then we can only prove that

*C*(3,

*r*) is enough.

**Information:**Please see the seminar webpage. This talk will be given in hybrid format.

**Vienna Research Seminar in Set Theory****Time:** Tuesday, 4 May, 11:30-13:00 CEST**Speaker:** L. Zdomskyy, TU Wien**Title:** Cardinalities of sets of reals satisfying combinatorial covering properties**Abstract:** We shall discuss which cardinalities sets of reals satisfying Menger and Hurewicz covering properties may have in some standard models of ZFC. Most of the results may be thought of as consistent instances of the Perfect Set Property, since they state that in some models, a set of reals satisfying certain covering properties either contains a copy of the Cantor set, or has small size. In particular, we plan to outline the proof of the fact that in the Sacks model every Menger totally imperfect set of reals has size at most ω1.

This is a joint work with V. Haberl and P. Szewczak.**Information:** This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

**Vienna Logic ColloquiumTime:** Thursday, 4 May, 15:00 – 15:45 CEST

**Speaker:**H. Mildenberger, University of Freiburg

**Title:**Destroying Guessing Principles

**Abstract:**An Ostaszewski club sequence is a weakening of Jensen’s diamond. In contrast to the diamond, the club does not imply the continuum hypothesis. Numerous questions about the club stay open, and we know only few models in which there is just a club sequence but no diamond sequence. In recent joint work with Shelah we found that a winning strategy for the completeness player in a bounding game on a forcing order does not suffice to establish the club in the extension.

**Information:**This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

**Cross-Alps Logic Seminar****Time:** Friday, 5 May, 16.00-17.00 CEST**Speaker:** D. Sinapova,** **Rutgers University**Title:** Mutual stationarity and the failure of SCH**Abstract:** Mutual stationarity is a compactness type property for singular cardinals. Roughly, it asserts that given a singular cardinal κ, stationary subsets of regular cardinals with limit κ have a “simultaneous witness” for their stationarity. This principle was first defined by Foreman and Magidor in 2001, who showed that it holds for every sequence of stationary sets of cofinality ω. They also showed that their ZFC result does not generalize to higher cofinality. Whether the principle can consistently hold for higher cofinalities remained open, until a few years ago Ben Neria showed that from large cardinals mutual stationarity at ⟨ℵn∣n<ω⟩ can be forced for any fixed cofinality.

We show that we can obtain mutual stationarity at ⟨ℵn∣n<ω⟩ for any fixed cofinality together with the failure of SCH at ℵω. This is joint work with Will Adkisson.**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, 5 May, 10:00am New York time (16:00 CEST)**Speaker:** Joel David Hamkins, Notre Dame University**Title:** Realizing Frege’s Basic Law V, provably in ZFC**Abstract:** The standard set-theoretic distinction between sets and classes instantiates in important respects the Fregean distinction between objects and concepts, for in set theory we commonly take the universe of sets as a realm of objects to be considered under the guise of diverse concepts, the definable classes, each serving as a predicate on that domain of individuals. Although it is commonly held that in a very general manner, there can be no association of classes with objects in a way that fulfills Frege’s Basic Law V, nevertheless, in the ZF framework, it turns out that we can provide a completely deflationary account of this and other Fregean abstraction principles. Namely, there is a mapping of classes to objects, definable in set theory in senses I shall explain (hence deflationary), associating every first-order parametrically definable class F with a set object εF, in such a way that Basic Law V is fulfilled:

εF=εG↔∀x(Fx↔Gx). Russell’s elementary refutation of the general comprehension axiom, therefore, is improperly described as a refutation of Basic Law V itself, but rather refutes Basic Law V only when augmented with powerful class comprehension principles going strictly beyond ZF. The main result leads also to a proof of Tarski’s theorem on the nondefinability of truth as a corollary to Russell’s argument. A central goal of the project is to highlight the issue of definability and deflationism for the extension assignment problem at the core of Fregean abstraction.**Information:** The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

**Toronto Set Theory Seminar****Time:** Friday, 5 May, 1.30-3.00 Toronto time (19.30-21.00 CEST)**Speaker:** Jeffrey Bergfalk, University of Barcelona**Title:** Applications of nontrivial coherence**Abstract:** This talk will survey some applications of infinitary combinatorics to superficially unrelated questions arising in the study of condensed mathematics, strong homology, and the derived limit functors, showing in the process that they all, combinatorially speaking, drink from the same well. At least as interesting as our ZFC answers to each of these questions are the further questions they open onto; we aim to survey these as well. This work is joint with Chris Lambie-Hanson, and carries a third aim of connecting with some of the material of his seminar talk of the preceding week; no dependency between the two talks, however, is intended.**Information:** Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

**CUNY Logic Workshop****Time:** Friday, 5 May, 2:00-3:30pm New York time (20:00-21:30 CEST)**Speaker: **Karen Lange, Wellesley College**Title: **Classification via effective lists**Abstract:** ‘Classifying’ a natural collection of structures is a common goal in mathematics. Providing a classification can mean different things, e.g., identifying a set of invariants that settle the isomorphism problem or creating a list of all structures of a given kind without repetition of isomorphism type. Here we discuss recent work on classifications of the latter kind from the perspective of computable structure theory. We’ll consider natural classes of computable structures such as vector spaces, equivalence relations, algebraic fields, and trees to better understand the nuances of classification via effective lists and its relationship to other forms of classification in this setting.**Information:** The talk will take place in person. For more information, please see the seminar webpage or email Victoria Gitman.