For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2021.
Caltech Logic Seminar
Time: Monday, 7 June, 12:00 – 1:00pm Pacific time (21:00 CET)
Speaker: Julien Melleray, Université Lyon 1
Title: A new proof of a theorem of Giordano, Putnam, and Skau
Abstract: A well-known result of Giordano-Putnam-Skau asserts that two minimal homeomorphisms of the Cantor space which have the same invariant Borel probability measures are orbit equivalent. I will present a new, rather elementary, proof of that fact, based on a strengthening of a 1979 theorem of Krieger concerning minimal actions of certain locally finite groups on the Cantor space. No familarity with topological dynamics will be assumed.
This is joint work with Simon Robert (Lyon).
Information: Check on the seminar webpage if the seminar will take place.
Time: Wednesday, 9 June, 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.
Münster research seminar on set theory
Time: Wednesday, 9 June, 15:15-16:45 CET
Speaker: Gunter Fuchs, CUNY)
Title: Fragments of (diagonal) strong reflection
Abstract: Continuation of last week’s talk.
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, 9 June, 16:00-17:30 CET
Speaker: Raffaella Cutolo, Università degli Studi di Napoli Federico II
Title: N-Berkeley cardinals and the two futures of set theory
Abstract: The talk will focus on Berkeley cardinals – the strongest known large
cardinal axioms – and their relativized version to inner models of ZFC, which
in fact play a decisive role in the current scenario of set theory. As we shall
see, by recent results of Woodin, there are just two, opposite possible futures
for set theory, and Berkeley cardinals are very involved in the question of
which of the two futures will prevail. In particular, the relativized version of
Berkeley cardinals turns out to be relevant with respect to that question, and
it is therefore worthy of attention.
We shall show the first example of the existence of a “N-Berkeley cardinal”
for an inner model N of ZFC, a result that is quite surprising as the involved
model N is a weak extender model, that is, N satisfies structural properties
making it very close to the set-theoretic universe V with respect to the large
cardinal axioms it is able to recognize; nevertheless, there exists (in V ) a
N-Berkeley cardinal, one that cannot exist in N, which models AC. We then
isolate a strong version of the notion of being N-Berkeley, and prove that
such strong version is inconsistent with the assumption that N is closed under
ω-sequences.
We finally illustrate the relevance of the results above with respect to the
crucial decision between the two futures of set theory.
Information: Online. If you wish to attend, please send an email to bagaria@ub.edu asking for the link.
Turin-Udine logic seminar
Time: Friday, 11 June, 16:30-18:30 CET
Speaker: Victoria Gitman, CUNY Graduate Center
Title: The old and the new of virtual large cardinals
Abstract: The idea of defining a generic version of a large cardinal by asking that some form of the elementary embeddings characterizing the large cardinal exist in a forcing extension has a long history. A large cardinal (typically measurable or stronger) can give rise to several natural generic versions with vastly different properties. For a \emph{generic large cardinal}, a forcing extension should have an elementary embedding j:V→Mof the form characterizing the large cardinal where the target model M is an inner model of the forcing extension, not necessarily contained in V. The closure properties on Mmust correspondingly be taken with respect to the forcing extension. Very small cardinals such as ω1 can be generic large cardinals under this definition. Quite recently set theorists started studying a different version of generic-type large cardinals, called \emph{virtual large cardinals}. Large cardinals characterized by the existence of an elementary embedding j:V→M typically have equivalent characterizations in terms of the existence of set-sized embeddings of the form j:Vλ→M. For a virtual large cardinal, a forcing should have an elementary embedding j:Vλ→M of the form characterizing the large cardinal with M∈Vand all closure properties on M considered from V’s standpoint. Virtual large cardinals are actually large cardinals, they are completely ineffable and more, but usually bounded above by an ω-Erd\H os cardinal. Despite sitting much lower in the large cardinal hierarchy, they mimic the reflecting properties of their original counterparts. Several of these notions arose naturally out of equiconsistency results. In this talk, I will give an overview of the virtual large cardinal hierarchy including some surprising recent directions.
Information: Please check on the semianr webpage if the seminar will take place. Online on WebEx. Please see the seminar webpage.
Toronto Set Theory Seminar
Time: Friday, 11 June, 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.
European Set Theory Society 