**Logic and Metaphysics Workshop**, CUNY**Time:** Monday, September 14th, 4.15-6.15pm (22.15 CEST) **For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu. Speaker:** Chris Scambler (NYU)

**Title:**Cantor’s Theorem, Modalized

**Abstract:**I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.

**Logic Seminar, Carnegie Mellon University****Time:** Tuesday, September 15, 3:30 – 4:30pm Eastern Daylight Time (21:00 CEST) **Speaker:** William Chan (Carnegie Mellon University)**Title:** A Survey of Combinatorics and Cardinality under Determinacy**Abstract: **We will survey some recent work with Jackson and Trang concerning combinatorics under the axiom of determinacy. We will be especially concerned with ultrapowers of the first uncountable cardinal by the partition measures and related questions concerning club uniformization and continuity of functions around the first uncountable cardinal. We will show that the cardinals below the power set of the first and second uncountable cardinals have a very complicated and rich structure under determinacy axioms. We will summarize our knowledge of this structure under AD, AD+, and the axiom of real determinacy.**Information:** Zoom link https://cmu.zoom.us/j/621951121, meeting ID: 621 951 121

**Bar-Ilan-****J****erusalem Set Theory Seminar****Time:** Wednesday, September 16, 11:00am Israel Time (10:00 CEST)**Speaker:** Uri Abraham, Ben-Gurion University**Title:** A simplified forcing for MA with a \Delta^2_1 well ordering of the reals**Abstract:** We present a result of the speaker and Shelah. The theorem is that one can force, over any model of Set Theory, MA +\Delta^2_1 well ordering of the reals. The difference from the previous proof is that for this simper proof, one assumes the existence of an inaccessible cardinal in the ground model.**Information:** Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

**Caltech Logic Seminar****Time:** Wednesday, September 16, 12:00 – 1:00pm Pacific time (21:00 CEST)**Speaker:** Steve Jackson, University of North Texas**Title:** Some complexity results in dynamics and number theory**Abstract:** The Ki-Linton theorem asserts that the set of base b normal numbers is a Π03-complete set. The base bb normal numbers can be viewed as the set of generic points for an associated dynamical system. This leads to the question of the complexity of the set of generic points for other numeration/dynamical systems, for example continued fractions, β-expansions, Lüroth expansions to name a few. We prove a general result which covers all of these cases, and involves a well-known property in dynamics, a form of the specification property. We then consider differences of these sets. Motivated by the descriptive set theory arguments, we are able to show that the set of continued fraction normal but not base b normal numbers is a complete D2(Π30) set. Previously, the best known result was that this set was non-empty (due to Vandehey), and this assumed the generalized Riemann hypothesis. The first part of the work is joint with Mance and Kwietniak, and the second part with Mance and Vandehey.

Information: Online talk https://caltech.zoom.us/j/95952118325?pwd=QzFPa3ZOeTJKWXJnSW5VbHhGOXJEZz09

**CUNY Logic Seminar (MOPA)****Time:** Wednesday, September 16, 5pm New York time (23:00 CEST) – note the time**Speaker: **Sam Coskey, Boise State University**Title:** Classification of countable models of ZFC**Abstract:** In 2009 Roman Kossak and I showed that the classification of countable models of PA is Borel complete, which means it is as complex as possible. The proof is a straightforward application of Gaifman’s canonical I-models. In 2017 Sam Dworetzky, John Clemens, and I showed that the argument may also be used to show the classification of countable models of ZFC is Borel complete too. In this talk I’ll outline the original argument for models of PA, the adaptation for models of ZFC, and briefly consider several subclasses of countable models of ZFC. **Information:** The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

**CUNY Set Theory Seminar****Time:** Friday, September 18, 14:00 New York time (20:00 CEST)**Speaker:** Arthur Apter, CUNY**Title:** UA and the Number of Normal Measures over ℵω+1**Abstract:** The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.**Information:** The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.