This is a list of online talks in set theory next week.

For a complete list see online activities. In case we missed an upcoming talk, please email matteo.viale@unito.it, boban.velickovic@math.univ-paris-diderot.fr or philipp.schlicht@bristol.ac.uk.

April 21

**Münster Set Theory Seminar** **Time:** Tuesday, April 21, 4:15pm CEST**Speaker:** Farmer Schlutzenberg, University of Münster**Title:** Non-definability of embeddings $j:V_\lambda\to V_\lambda$**Abstract:** Assume $\ZF$. We show that there is no limit ordinal $\lambda$ and $\Sigma_1$-elementary $j:V_\lambda\to V_\lambda$ which is definable from parameters over $V_\lambda$.**Information:** The seminar will be held remotely via zoom. Please contact rds@wwu.de ahead of time in order to participate.

April 22

**New York Logic Seminar** (MOPA)**Time:** Wednesday, April 22, 7pm New York time (Thursday, April 23, 1am CEST)**Speaker:** Corey Switzer, CUNY**Title:** **Hanf Numbers of Arithmetics****Abstract:** Recall that given a complete theory T and a type p(x) the *Hanf number for* p(x) is the least cardinal κ so that any model of T of size κ realizes p(x) (if such a κ exists and ∞ otherwise). The *Hanf number for* T, denoted H(T), is the supremum of the successors of the Hanf numbers for all possible types p(x) whose Hanf numbers are <∞. We have seen so far in the seminar that for any complete, consistent T in a countable language H(T)≤ℶω1 (a result due to Morley). In this talk I will present the following theorems: (1) The Hanf number for true arithmetic is ℶω (Abrahamson-Harrington-Knight) but (2) the Hanf number for False Arithmetic is ℶω1 (Abrahamson-Harrington)**Information:** The seminar will take place virtually. Please email Victoria Gitman for the meeting id.

**Bar-Ilan University and Hebrew University Set Theory Seminar** **Time:** Wednesday, April 22, 11am IST (10am CEST) **Speaker:** Jing Zhang**Title:** Transformations of the transfinite plane**Abstract:** We discuss the existence of certain transformation functions turning pairs of ordinals into triples (or pairs) of ordinals, that allows reductions of complicated Ramsey theoretic problems into simpler ones. We will focus on the existence of various kinds of strong colorings. The basic technique is Todorcevic’s walks on ordinals. Joint work with Assaf Rinot.**Information:** The zoom meeting ID is 243-676-331 and no password.

April 23

**Kurt Gödel Research Center Seminar** (organised by Ben Miller)**Time:** Thursday, April 23, 16:00 CEST

**Speaker:**Noé de Rancourt, KGRC

**Title:**Weakly Ramsey ultrafilters

**Abstract:**Weakly Ramsey ultrafilters are ultrafilters on ωω satisfying a weak local version of Ramsey’s theorem; they naturally generalize Ramsey ultrafilters. It is well known that an ultrafilter on ωω is Ramsey if and only if it is minimal in the Rudin-Keisler ordering; in joint work with Jonathan Verner, we proved that similarly, weakly Ramsey ultrafilters are low in this ordering: there are no infinite chains below them. This generalizes a result of Laflamme’s. In this talk, I will outline a proof of this result, and the construction of a counterexample to the converse of this fact, namely a non-weakly Ramsey ultrafilter having exactly one Rudin-Keisler predecessor. This construction is partly based on finite combinatorics.

**Information:**Talk via zoom.

April 24

**CUNY Set Theory Seminar****Time:** Friday, April 24, 2pm New York time (8pm CEST)**Speaker:** Arthur Apter, CUNY**Title:** Indestructibility and the First Two Strongly Compact Cardinals**Abstract:** Starting from a model of ZFC with two supercompact cardinals, I will discuss how to force and construct a model in which the first two strongly compact cardinals κ1 and κ2 are also the first two measurable cardinals. In this model, κ1’s strong compactness is indestructible under arbitrary κ1-directed closed forcing, and κ2’s strong compactness is indestructible under Add(κ2,λ) for any ordinal λ. This answers a generalized version of a question of Sargsyan.**Information:** The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.