The announcements are updated continuously. For a list of talks in the coming weeks, see https://ests.wordpress.com/online-activities-2022.

**Vienna Research Seminar in Set Theory****Time:** Tuesday, 29 November, 15:00-16:30 CET**Speaker:** Corey Switzer, Universität Wien **Title:** Subversion Forcing, part 2**Abstract:** In these two talks we will introduce Jensen’s classes of subcomplete and subproper forcing as well as discuss some applications due to the speaker and Fuchs, and the speaker and Sakai. An important feature of proper forcing is the countable covering property: every countable set of ordinals added by a proper forcing notion is contained in a ground model countable set of ordinals. This is important in iteration theorems. Subproper forcing is a weakening of proper forcing that is still iterable while including some well known forcing notions which do add countable sets of ordinals that are not covered by anything in the ground model including Namba forcing (under CH) and Prikry forcing. One can weaken other classes of forcing notions in a similar way and the “sub”version of the countably closed forcing, known as subcomplete forcing, is a particularly interesting subclass of subproper forcing that was used by Jensen in several applications including his solution to the extended Namba problem.

In the first of these talks I will introduce the classes subproper and subcomplete forcing as well as discuss simplifications of them due to Fuchs and myself. Time permitting I will discuss new iterations theorems for these classes reminiscent of similar theorems proved for proper forcing in the context of the reals and combinatorics on ω1 (ωω-bounding, preservation of Souslin trees etc). In the second talk I will discuss the forcing axioms for these classes including their applications and limitations. In particular, time permitting, I will discuss a recent result, joint with Hiroshi Sakai that the forcing axiom for subcomplete forcing is compatible with a □ω1-sequence. The take away is a class of strong forcing axioms that are compatible with a wide variety of behaviour on the level of the reals and combinatorics on cardinals below the continuum.**Information:** This talk will be given in hybrid format. Please contact Richard Springer for information how to participate.

**Baltic Set Theory Seminar****Time:** Tuesday, 29 November, 15:00-16:30 CET**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. Sandra Müller, Stationary-tower-free proof of Woodin’s Sealing Theorem.

2. Matteo Viale, Generic absoluteness theorem for the omega_1 Chang model conditioned to MM^{+++}.**Information:** Please see the seminar webpage.

**CMU Core Model Theory Seminar****Time:** Tuesday, 29 November, 1:30 – 3:00pm Pittsburgh time (19:30 – 21:00 CET) **Speaker:** Benjamin Siskind, Carnegie Mellon University**Title:** Full normalization and HOD^L(R)**Abstract: **We’ll review some aspects of the HOD analysis of L(R) and

introduce the full normalization machinery developed by Steel and

Schlutzenberg. We’ll use this to show that HOD^L(R)|theta is actually a

normal iterate of M_omega|delta via M_omega’s canonical iteration strategy

(and a bit more), a result of Steel and Schlutzenberg. Time permitting, we

may discuss other applications of full normalization, due to Steel.**Information:** Please contact Ernest Schimmerling in advance for the zoom link.

**CMU Logic Seminar****Time:** Tuesday, 29 November, 3:30 – 4:30pm Pittsburgh time (21:30 – 22:30 CET) **Speaker:** Verónica Becher, University of Buenos Aires**Title:** Turing’s Normal Numbers**Abstract: **In a manuscript entitled “A note on normal numbers” and written

presumably in 1937 Alan Turing gave an algorithm that produces real

numbers normal to every integer base. This proves, for the first time, the

existence of computable instances and provides an answer to Borel’s

problem on giving examples of normality. Furthermore, with this work

Turing pioneers the theory of randomness and shows that he had the

insight, ahead of his time, that traditional mathematical concepts, like

measure or continuity, could be made computational. In this talk I will

highlight the ideas in these achievements of Turing, which are largely

unknown because his manuscript remained unpublished until it appeared in

his Collected Works in 1992.**Information:** See the seminar webpage.

**Helsinki Logic Seminar****Time:** Wednesday, 30 November, 12:00 – 14:00 Helsinki time (11:00-13:00 CET)**Speaker:** Miika Hannula**Title:** tba**Abstract:** tba**Information:** The talk will take place in hybrid mode. Please see the seminar webpage for the link.

**Leeds Models and Sets Seminar****Time:** Wednesday, 30 November, 13:45-15:00 local time (14:45-16:00 CET)**Speaker:** Thilo Weinert, University of Vienna**Title:** Two New Inequalities for Cardinal Characteristics of the Continuum**Abstract:** Over the last decades the theory of cardinal characteristics of the continuum has emerged as one among several important subfields of set theory. Some of the classical results in it precede the invention of forcing and arguably the aforementioned emergence. Open problems in this field have inspired the invention over ever more versatile constructions of forcing notions and much of the progress has consisted of proving the values of cardinal characteristics not to be ZFC-provably related. A recent outlier has been the celebrated result by Malliaris and Shelah that p is equal to t. I had guessed that there might be more ZFC-provable relations between the hitherto defined characteristics and I am going to talk about what I found up to now. This is to say that I am going to present some ZFC-provable inequalities. In particular I am going to show that the evasion number is at most the subseries number. These cardinal characteristics have been introduced in work by Blass, Brendle, Brian, and Hamkins and originate from Algebra and Analysis, respectively. The proof interpolates via the pair-splitting number which is due to Minami.**Information:** Please see the seminar webpage.

**Caltech Logic Seminar****Time:** Wednesday, 30 November, 11:00am-12:00pm Pacific time (20:00-21:00 CET)**Speaker:** Sumun Iyer, Cornell**Title:** Dynamics of the Knaster continuum homeomorphism group**Abstract:** We use the projective Fraissé approach and Ramsey’s theorem to show that the universal minimal flow of the homeomorphism group of the universal Knaster continuum is homeomorphic to the universal minimal flow of the free abelian group on countably many generators. We will define a projective Fraissé class whose limit approximates the universal Knaster continuum in such a way that the group Aut(K)Aut(K) of automorphisms of the Fraissé limit is a dense subgroup of the group, Homeo(K)Homeo(K), of homeomorphisms of the universal Knaster continuum. The computation of the universal minimal flow involves modifying the Fraissé class in a natural way so that it approximates an open, normal, extremely amenable subgroup of Homeo(K)Homeo(K).**Information:** Please see the seminar webpage.

**Cross-Alps Logic Seminar****Time:** Friday, 2 December 16.00-18.00 CET**Speaker:** F. Parente, University of Turin**Title:** Good ultrafilters and universality properties of forcing**Abstract:** In 1964, Keisler introduced κ-good ultrafilters, which can be characterized as those ultrafilters which produce κ-saturated ultrapowers. The problem of finding an analogous characterization for ultrafilters on Boolean algebras has been considered by Mansfield (1971), Benda (1974), and Balcar and Franek (1982), who proposed and compared different notions of “goodness” for such ultrafilters. In the first part of my talk, I shall outline the different definitions introduced in the literature and show that they are in fact all equivalent, thus providing a complete characterization of those ultrafilters which produce κ-saturated Boolean ultrapowers. In the second part of the talk, I shall present a joint work with Matteo Viale, which started in 2015 during my Master’s thesis and was recently revived during the last few months in Torino. The aim of our project is to study the universality properties of forcing. More precisely, we shall prove that, for many interesting signatures, every model of the universal theory of an initial segment of the universe can be embedded into a model constructed by forcing. To achieve this goal, we build good ultrafilters on forcing notions such as the Lévy collapsing algebra and Woodin’s stationary tower.**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, 2 December, 12:30pm New York time (18:30 CET)**Speaker: **Will Boney, Texas State University**Title:** tba**Abstract:** tba**Information:** The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

**Toronto Set Theory Seminar****Time:** Friday, 2 December, 1.30-3.00 Toronto time (19.30-21.00 CET)**Speaker:** Eduardo Duenez, University of Texas at San Antonio, and Jose Iovino, University of Texas at San Antonio**Title:** tba**Abstract:** tba**Information:** Please see http://gfs.fields.utoronto.ca/activities/22-23/set-theory-seminar.

**CUNY Logic Workshop****Time:** Friday, 2 December, 2:00 – 3:30 New York time (20:00-21:30 CET)**Speaker: **Michał Tomasz Godziszewski, University of Vienna**Title: **tba**Abstract:** tba**Information:** The talk will take place in hybrid mode. Please see the seminar webpage or email Victoria Gitman for the link.