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

This week’s special event: **Third Colloquium of the European Set Theory Society****Time:** Thursday, 11 May, 17:00-19:00 CEST

**Vienna Research Seminar in Set Theory****Time:** Tuesday, 9 May, 15:00-16:30 CEST**Speaker:** Thilo Weinert, Universität Wien**Title:** On Unsound Linear Orderings**Abstract:** In the Eighties Adrian Mathias introduced the notion of soundness of an ordinal. An ordinal is sound if for any countable partition P of it only countably many ordinals are order-types of unions of subpartitionts of P. Mathias showed that the least unsound ordinal ζ is ωω+21 if ℵ1 can be embedded into the continuum but if ℵ1 is regular yet cannot be embedded into the continuum, ζ⩾ωω2+11.

I am going to discuss his findings and consider the notion for the more general class of linear orderings building on work by him, MacPherson, and Schmerl. I am also going to mention some open problems. This is joint ongoing work with Garrett Ervin and Jonathan Schilhan.**Information:** This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

**Baltic Set Theory Seminar****Time:** Tuesday, 9 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, 10 May, 13:00-15:00 Israel Time (12:00-14:00 CEST)**Speaker:** Jouko Vaananen**Title:** Descriptive Set Theory in Generalized Baire Spaces**Abstract:** I will review the motivation and basic notions of Generalized Baire Spaces. I will then talk about the role of trees, such as wide Aronszajn trees, in the Descriptive Set Theory of Generalized Baire Spaces. This part is motivated by recent joint work with Omer Ben-Neria and Menachem Magidor. I will also talk about universally Baire sets in Generalized Baire Spaces. This part is joint work with Menachem Magidor.**Information:** Contact Menachem Magidor or Omer Ben-Neria ahead of time for the zoom link.

**Leeds Models and Sets Seminar****Time:** Wednesday, 10 May, 13:45-15:00 local time (14:45-16:00 CEST)**Speaker:** Victoria Gould, University of York**Title:** Pseudo-finite semigroups and diameter**Abstract:** A semigroup S is said to be (right) pseudo-finite if the universal right congruence S x S can be generated by a finite set U of pairs of elements of S and there is a bound on the length of derivations for an arbitrary pair as a consequence of those in U . The diameter of a pseudo-finite semigroup is the smallest such bound taken over all finite generating sets.

The notion of being pseudo-finite was introduced by White in the language of ancestry, motivated by a conjecture of Dales and Zelazko for Banach algebras. The property also arises from several other sources.

Without assuming any prior knowledge, this talk investigates the somewhat unpredictable notion of pseudo-finiteness. Some well-known uncountable semigroups have diameter 1; on the other hand, a pseudo-finite group is forced to be finite. Actions, presentations, Rees matrix constructions and some good old-fashioned semigroup tools all play a part.

This research sits in the wider framework of a study of finitary conditions for semigroups.**Information:** Please see the seminar webpage.

**Caltech Logic Seminar****Time:** Wednesday, 10 May, 12:00am-13:00pm Pacific time (21:00-22:00 CEST)**Speaker:** Allison Wang, CMU**Title:** Every CBER is smooth below the Carlson-Simpson generic partition**Abstract:** One difficulty that arises in studying the class of countable Borel equivalence relations (CBERs) is that in many cases, the complexity of a CBER lies on a “small” set. For instance, a result of Hjorth and Kechris states that every CBER on a Polish space is hyperfinite when restricted to some comeager set. Another result, due to Mathias, shows that every CBER on the Ellentuck Ramsey space is hyperfinite when restricted to some pure Ellentuck cube. In this talk, we will show that every CBER on the space of all infinite partitions of the natural numbers coincides with equality below a Carlson-Simpson generic element. This is joint work with Aristotelis Panagiotopoulos.**Information:** Please see the seminar webpage.

**Third Colloquium of the European Set Theory Society****Time:** Thursday, 11 May, 17:00-19:00 CEST**Panelists:** Alan Dow, University of North Carolina at Charlotte

Heike Mildenberger, University of Freiburg

Slawek Solecki, Cornell University

Matteo Viale, University of Torino**Title:** European Set Theory Society Panel Discussions**Abstract:** Four experts will describe the general area they represent, explain where the area is heading and discuss how it relates to other areas of set theory and mathematics.**Information:** Online. Zoom link for 11 May: https://univienna.zoom.us/j/61733153940?pwd=Wm5sNjczVTlUWVA3Vy9pZlZreFlDQT09

**CUNY Set Theory Seminar****Time:** Friday, 12 May, 12:30pm New York time (18:30 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.

**CUNY Logic Workshop****Time:** Friday, 12 May, 2:00 – 3:30 New York time (20:00-21:30 CEST)**Speaker: **Brian Wynne, CUNY**Title: **Recent developments in the model theory of Abelian lattice-ordered groups**Abstract:** An Abelian lattice-ordered group (ℓ-group) is an Abelian group with a partial ordering, invariant under translations, that is a lattice ordering. A prototypical example of an ℓ-group is C(X), the continuous real-valued functions on the topological space X with pointwise operations and ordering. Let A be the class of ℓ-groups, viewed as structures for the first-order language L={+,−,0,∧,∨}. After giving more background on ℓ-groups, I will survey what is known about the ℓ-groups existentially closed (e.c.) in A, including some new examples I constructed using Fraïssé limits. Then I will discuss some recently published work of Scowcroft concerning the ℓ-groups e.c. in W+, the class of nonzero Archimedean ℓ-groups with distinguished strong order unit (viewed as structures for L1=L∪{1}). Building on Scowcroft’s results, I will present new axioms for the ℓ-groups e.c. in W+ and show how they allow one to characterize those spaces X for which (C(X),1X) is e.c. in W+.**Information:** The talk will take place in person. For more information, please see the seminar webpage or email Victoria Gitman.