Online activities 21-26 September 2020

Caltech Logic Seminar
Time: Wednesday, September 23, 12:00 – 1:00pm Pacific time (21:00 CEST)
Speaker: Dana Bartošová, University of Florida
Title: On phase spaces of universal minimal flows of groups with compact normal subgroups
Abstract: For a topological group G, a G-flow is a continuous action of G on a compact Hausdorff space X; we call X the phase space of the G-flow. A G-flow on X is minimal if X has no closed non-trivial invariant subset. The universal minimal G-flow, M(G), has every minimal G-flow as a quotient and it is unique up to isomorphism. We show that whenever we have a short exact sequence 0→K→G→H→0 of topological groups with the image of K a compact normal subgroup of G, then the phase space of M(G) is homeomorphic to the product of the phase space of M(H) with K. For instance, if G is a Polish, non-Archimedean group, and the image of K is open in G, then H is a countable discrete group. The phase space of M(H) is homeomorphic to Gl⁡(22ℵ0), the Stone space of the completion of the free Boolean algebra on 2ℵ0 generators by Balcar-Błaszczyk and Glasner-Tsankov-Weiss-Zucker. Therefore, the phase space of M(G) is homeomorphic to K×Gl⁡(22ℵ0). When the sequence splits, that is, G≅H⋉K, then the homeomorphism witnesses an isomorphism of flows, recovering a result of Kechris and Sokić.
Information: Online talk https://caltech.zoom.us/j/99296122790?pwd=bUN4RS94RVYrTEtGTGhqTHRJbm9nZz09

Southern Illinois University Logic Seminar
Time: Thursday, September 24, 1pm US Central Daylight Time (20:00 CEST)  
Speaker: Arno Pauly, Swansea University
Title: How computability-theoretic degree structures and topological spaces are related
Abstract: We can generalize Turing reducibility to points in a large class of topological spaces. The point degree spectrum of a space is the collection of the degrees of its points. This is always a collection of Medvedev degrees, and it turns out that topological properties of the space are closely related to what degrees occur in it. For example, a Polish space has only Turing degrees iff it is countably dimensional. This connection can be used to bring topological techniques to bear on problems from computability theory and vice versa. The talk is based on joint work with Takayuki Kihara and Keng Meng Ng (https://arxiv.org/abs/1405.6866 and https://arxiv.org/abs/1904.04107).
Information: The seminar will take place virtually via zoom.

CUNY Set Theory Seminar
Time: Friday, September 25, 11:00 New York time (17:00 CEST)
Speaker: Ralf Schindler, University of Münster
Title: Martin’s Maximum^++ implies the P_max axiom (*)
Abstract: Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and ‘consistent’ needs to mean ‘consistent in a strong sense.’ It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler’s ‘consistency properties’.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Online activities 14-20 September 2020

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-Jerusalem 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.

Online activities 7-13 September 2020

Genoa Logic Seminar
Time: Tuesday, September 8, 17:00-18:00 CEST
Speaker: Gianluca Basso, Université de Lausanne
Title: Topological dynamics beyond Polish groups
Abstract: When $G$ is a Polish group, one way of knowing that it has “nice” dynamics is to show that $M(G)$, the universal minimal flow of $G$, is metrizable. For non-Polish groups, this is not the relevant dividing line: the universal minimal flow of $\mathrm{Sym}(\kappa)$ is the space of linear orders on $\kappa$—not a metrizable space, but still “nice”—, for example.
In this talk, we present a set of equivalent properties of topological groups which characterize having “nice” dynamics. We show that the class of groups satisfying such properties is closed under some topological operations and use this to compute the universal minimal flows of some concrete groups, like $\mathrm{Homeo}(\omega_{1})$. This is joint work with Andy Zucker.
Information: The seminar will take place on Microsoft Teams, at the page of the Genoa logic group. The access code is fpedcxn. Alternatively, you can write to camerlo@dima.unige.it to have an access link. Further information on the activities of the Genoa logic group can be found at http://www.dima.unige.it/~camerlo/glhome.html
Note: Due to the current emergency situation, the web page might not be updated.

CUNY Logic Seminar (MOPA)
Time: Wednesday, September 9, 3pm New York time (21:00 CEST) – note the time
Speaker: Saeideh Bahrami, Institute for Research in Fundamental Sciences, Tehran
Title: Fixed Points of Initial Self-Embeddings of Models of Arithmetic
Abstract: In 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Southern Illinois University Logic Seminar
Time: Thursday, 10 September, 1pm US Central Daylight Time (20:00 CEST)  
Speaker: Mirna Džamonja (IHPST, CNRS-Université Panthéon-Sorbonne Paris, France)
Title: On logics that make a bridge from the Discrete to the Continuous
Abstract: We study logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence.
Information: The seminar will take place virtually via zoom.

Online activities 17-23 August 2020

Paul Bernays Lectures 2020: Struggling with the size of infinity, Lecture 1
Time: Monday, August 31, 17:00 CEST
Speaker: Prof. Saharon Shelah, Hebrew University Jerusalem
Title: Cardinal arithmetic: Cantor’s paradise
Abstract: We will explain Hilbert’s first problem. Specifically, this asks what the value of the continuum is: Is the number of real numbers equal to aleph1 — the first infinite cardinal above aleph0=the number of natural numbers? Recall that Cantor introduces infinite numbers just as equivalence classes of sets under “there is a bijection”. The problem of the size of the continuum really means: ”What are the laws of cardinal arithmetic, i.e. the arithmetic of infinite numbers”. We will review its history, (including Gödel and Cohen), mention different approaches, explain what is undecidable, and mainly present some positive answers which we have nowadays. Those will be mainly about cofinality arithmetic, the so called pcf theory; but we will also mention cardinal invariants of the continuum.
Information: Due to the unusual circumstances of the COVID-​​19 pandemia, the Paul Bernays Lectures 2020 will take place as a webinar: Link for this webinar. All lectures are given in English and are self-​contained. Lecture 1 is aimed at a general audience; lecture 2 and 3 address the scientific community.

Paul Bernays Lectures 2020: Struggling with the size of infinity, Lecture 2
Time: Tuesday, September 1, 14:15 CEST
Speaker: Prof. Saharon Shelah, Hebrew University Jerusalem
Title: How large is the continuum?
Abstract: Cantor discovered that in mathematics we can distinguish many infinities, called the aleph numbers. The works of Gödel and Cohen told us that we cannot decide what the value of the continuum is, that is, which of the aleph numbers is the answer to the question “How many real numbers are there?”. This still does not stop people from having opinions and arguments. One may like to assume extra axioms which will decide the question (usually as aleph1 or aleph2), and argue that they should and eventually will be adopted. We feel that assuming the continuum is small makes us have equalities which are incidental. So if we can define 10 natural cardinals which are uncountable but at most the continuum, and the continuum is smaller than aleph10, at least two of them will be equal, without any inherent reasons. Such numbers are called cardinal invariants of the continuum, and they arise naturally from various perspectives. We would like to show that they are independent, that is, that there are no non-​trivial restrictions on their order. More specifically, we shall try to explain the Cichon diagram and what we cannot tell about it.
Information: Due to the unusual circumstances of the COVID-​​19 pandemia, the Paul Bernays Lectures 2020 will take place as a webinar: Link for this webinar. All lectures are given in English and are self-​contained. Lecture 1 is aimed at a general audience; lecture 2 and 3 address the scientific community.

Paul Bernays Lectures 2020: Struggling with the size of infinity, Lecture 3
Time: Tuesday, September 1, 16:30 CEST
Speaker: Prof. Saharon Shelah, Hebrew University Jerusalem
Title: Cardinal invariants of the continuum: are they all independent?
Abstract: Experience has shown that in almost all cases, if you define a bunch of cardinal invariants of the continuum, then modulo some easy inequalities, it follows by forcing (the method introduced by Cohen) that there are no more restrictions. Well, those independence results have been mostly for the case of the continuum being at most aleph2. But this seems to be just due to our lack of ability, as the problems are harder. However, this opinion ignores the positive side of having forcing, of us being able to prove independence results: clearing away the rubble of independence results, the cases where we fail may indicate that there are theorems there. We shall on the one hand deal with cases where this succeeds and on the other hand with cofinality arithmetic, and what was not covered in the first lecture.
Information: Due to the unusual circumstances of the COVID-​​19 pandemia, the Paul Bernays Lectures 2020 will take place as a webinar: Link for this webinar. All lectures are given in English and are self-​contained. Lecture 1 is aimed at a general audience; lecture 2 and 3 address the scientific community.

CUNY Logic Seminar (MOPA)
Time: Wednesday, September 2, 14:00 New York time (20:00 CEST) – note the time
Speaker: Petr Glivický, Universität Salzburg
Title: The ω-iterated nonstandard extension of N and Ramsey combinatorics
Abstract: In the theory of nonstandard methods (traditionally known as nonstandard analysis), each mathematical object (a set) x has a uniquely determined so called nonstandard extension ∗x. In general, ∗x⊋{∗y;y∈x} – that is, besides the original ‘standard’ elements ∗y for y∈x, the set ∗x contains some new ‘nonstandard’ elements. 
For instance, some of the nonstandard elements of ∗R can be interpreted as infinitesimals (there is ε∈∗R such that 0<ε<1/n for all n∈N) allowing for nonstandard analysis to be developed in ∗R, while ∗N turns out to be an (at least ℵ1-saturated) nonstandard elementary extension of N (in the language of arithmetic).
While the whole nonstandard real analysis is most naturally developed in ∗R (with just a few advanced topics where using the second extension ∗∗R is convenient, though far from necessary), recent successful applications of nonstandard methods in combinatorics on N have utilized also higher order extensions (n)∗N=∗∗∗⋯∗N with the chain ∗∗∗⋯∗ of length n>2.
In this talk we are going to study the structure of the ω-iterated nonstandard extension ⋅N=⋃n∈ω(n)∗N of N and show how the obtained results shed new light on the complexities of Ramsey combinatorics on N and allow us to drastically simplify proofs of many advanced Ramsey type theorems such as Hindmann’s or Milliken’s and Taylor’s.
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 4, 14:00 New York time (20:00 CEST)
Speaker: Mirna Džamonja, IHPST, CNRS-Université Panthéon-Sorbonne Paris
Title: On logics that make a bridge from the Discrete to the Continuous
Abstract: We study logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

Paul Bernay Lectures 2020 (Online)

The Paul Bernays Lectures 2020 at ETH Zürich will take place as an online Webinar August 31- September 1.

Prof. Saharon Shelah, Hebrew University Jerusalem, Israel, will speak about Struggling with the Size of Infinity.

Please see here for more information.

Online activities 17-23 August 2020

ALGOS 2020 – ALgebras, Graphs and Ordered Sets – August 26th to 28th (Online)
Time: Wednesday, August 26, 9:30am – Friday, August 29, 19:30pm, CEST
Information: Please see here for the program and advance registration.

Bar-Ilan-Jerusalem Set Theory Seminar
Time: Wednesday, August 26, 11:00am Israel Time (10:00 CEST)
Speaker: Menachem Magidor, Hebrew University
Title: Around weak diamond and uniformization
Abstract: I’ll present some old results about weak diamond, uniformization and maybe some connections to Whitehead problem. In particular I’ll present Woodin’s elegant proof to the Devlin-Shelah equivalence of Weak diamond with 2^\aleph_0<2^\aleph_1.
Information: Contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

CUNY Logic Seminar (MOPA)
Time: Wednesday, August 26, 12:00 New York time (18:00 CEST) – note the time
Speaker: Emil Jeřábek, Czech Academy of Sciences
Title: Feasible reasoning with arithmetic operations
Abstract: In bounded arithmetic, we study weak fragments of arithmetic that often correspond in a certain sense to computational complexity classes (e.g., polynomial time). Questions about provability in such theories can be thought of as a form of feasible reasoning: considering a natural object of interest from a complexity class C, can we prove its fundamental properties using only concepts from C?
Our objects of interest in this talk will be the elementary integer arithmetic operations +,−,×,/, whose complexity class is (uniform) TC0, a small subclass of P. The corresponding arithmetical theory is VTC0. Since we do not know yet if the theory can prove the totality of division and iterated multiplication ∏i<nXi which are in TC0 by an intricate result of Hesse, Allender, and Barrington, we will also consider an extension of the theory VTC0+IMUL.
Our main question is what can VTC0±IMUL prove about the elementary arithmetic operations. The answer is that more than one might expect: VTC0+IMUL proves induction for quantifier-free formulas in the basic language of arithmetic (IOpen), and even induction and minimization for Σb0 (sharply bounded) formulas in Buss’s language. This result is connected to the existence of TC0 constant-degree root-finding algorithms; the proof relies on a formalization of a form of the Lagrange inversion formula in VTC0+IMUL, and on model-theoretic abstract nonsense involving valued fields.
The remaining problem is if VTC0 proves IMUL. We will discuss issues with formalization of the Hesse–Allender–Barrington construction in VTC0, and some partial results (this is a work in progress).
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

CUNY Set Theory Seminar
Time: Friday, August 28, 14:00 New York time (20:00 CEST)
Speaker: Miha Habic, Bard College at Simon’s Rock
Title: Normal ultrapowers with many sets of ordinals
Abstract: Any ultrapower M of the universe by a normal measure on a cardinal κ is quite far from V in the sense that it computes V_κ+2 incorrectly. If GCH holds, this amounts to saying that M is missing a subset of κ+. Steel asked whether, even in the absence of GCH, normal ultrapowers at κ must miss a subset of κ+. In the early 90s Cummings gave a negative answer, building a model with a normal measure on κ whose ultrapower captures the entire powerset of κ+. I will present some joint work with Radek Honzík in which we improved Cummings’ result to get this capturing property to hold at the least measurable cardinal.
Information: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id (this talk will have a different meeting ID!).

ALGOS 2020 – ALgebras, Graphs and Ordered Sets – August 26th to 28th (Online)

The conference ALGOS 2020 ALgebras, Graphs and Ordered Sets will take place online from August 26th to 28th, 2020.

To receive news and further information on the online event, please register.

Originating in arithmetics and logic, the theory of ordered sets is now a field of combinatorics that is intimately linked to graph theory, universal algebra and multiple-valued logic, and that has a wide range of classical applications such as formal calculus, classification, decision aid and social choice.

This international conference « Algebras, graphs and ordered sets » (ALGOS 2020) will bring together some of the best specialists in the theory of graphs, relational structures and ordered sets, themes that are omnipresent in artificial intelligence and in knowledge discovery, and with concrete applications in biomedical sciences, security, social networks and e-learning systems. One of the goals of this event is to provide a common ground for researchers in various fields of computer science and mathematics to meet, present their latest results, and discuss original applications in related scientific fields. On this basis, we hope for fruitful exchanges that can motivate multidisciplinary projects.

ALGOS 2020 is dedicated to Maurice Pouzet on the occasion of his 75th birthday.

Maurice Pouzet is Emeritus Professor of the University Claude-Bernard Lyon 1 and adjunct-professor of the University of Calgary (Canada).

ALGOS 2020 will be on August 26 (Wednesday), 27 (Thursday), 28 (Friday) of 2020, and was planned to take place at the Lorraine Research Laboratory in Computer Science and its Applications (LORIA, UMR 7503). Due to the COVID-19 pandemic, ALGOS 2020 will take place online. To receive news and further information on the online event, please register.

There will be several presentations (keynote/regular). In addition to the local proceedings from LORIA (Université de Lorraine, CNRS, Inria Nancy G.E.), three special journal volumes are have been confirmed in the Journal of Multiple-Valued Logic and Soft-Computing, Discrete Mathematics & Theoretical Computer Scienceand Order for selected contributions.

Online activities 17-23 August 2020

Bar-Ilan-Jerusalem Set Theory Seminar
Time: Wednesday, August 19, 11:00am Israel Time (10:00 CEST)
Speaker: Uri Abraham, Ben-Gurion University
Title: Coding well ordering of the reals with ladders, part 5 
Abstract: Results from the 2002 paper “Coding with Ladders a Well Ordering of the Reals” by Abraham and Shelah.
Information: contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

CUNY Logic Seminar (MOPA)
Time: Wednesday, August 19, 14:00 New York time (20:00 CEST) – note the time
Speaker: Leszek Kołodziejczyk, University of Warsaw
Title: Ramsey’s Theorem over RCA_0*
Abstract: The usual base theory used in reverse mathematics, RCA0, is the fragment of second-order arithmetic axiomatized by Δ01 comprehension and Σ01 induction. The weaker base theory RCA∗0 is obtained by replacing Σ01 induction with Δ01 induction (and adding the well-known axiom exp in order to ensure totality of the exponential function). In first-order terms, RCA0 is conservative over IΣ1 and RCA∗0 is conservative over BΣ1+exp. 
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey’s Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey’s Theorem over RCA∗0.Given standard natural numbers n,k≥2, let RTnk stand for Ramsey’s Theorem for k-colourings of n-tuples. We first show that assuming the failure of Σ01 induction, RTnk is equivalent to its own relativization to an arbitrary Σ01-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnk for n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2k. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22 over the traditional base theory RCA0.
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

CUNY Set Theory Seminar
Time: Friday, August 21, 14:00 New York time (20:00 CEST)
Speaker: Dan Hathaway University of Vermont
Title: A relative of ZF+DC+‘ω1 is measurable’
Abstract: Let Φ be the statement that for any function f:ω1×ω1→ω, there are functions g1,g2:ω1→ω such that for all (x,y)∈ω1×ω1, we have f(x,y)≤max {g1(x),g2(y)}. We will show that Φ follows from ZF+DC+‘ω1 is measurable’. On the other hand using core models, we will show that Φ+‘the club filter on ω1 is normal’ implies there are inner models with many measurable cardinals. We conjecture that Φ and ZF+DC+‘ω1 is measurable’ have the same consistency strength. The research is joint with Francois Dorais at the University of Vermont.
Information: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id (this talk will have a different meeting ID!).

2020 Fudan Logic Summer School (Online)

The 2020 Fudan Logic Summer School (Online) takes place August 10 – August 21, 2020.

The first week (Aug 10 – Aug 14): Nonstandard analysis (Renling Jin 金人麟, in Chinese)

The second week (Aug 17 – Aug 21): Set theory – Forcing axioms and the ℙmax axiom (∗) (Ralf Schindler)

Please find the schedule here.

Please email Zhaokuan Hao at  zkhao@fudan.edu.cn  in order to register and get the meeting ID.

Online activities 10-16 August 2020

Bar-Ilan-Jerusalem Set Theory Seminar
Time: Wednesday, August 12, 11:00am Israel Time (10:00 CEST)
Speaker: Uri Abraham, Ben-Gurion University
Title: Coding well ordering of the reals with ladders, part 4 
Abstract: Results from the 2002 paper “Coding with Ladders a Well Ordering of the Reals” by Abraham and Shelah.
Information: contact Menachem Magidor, Asaf Rinot or Omer Ben-Neria ahead of time for the zoom link.

CUNY Logic Seminar (MOPA)
Time: Wednesday, August 12, 19:00 New York time (1:00am July 30 CEST) – note the time
Speaker: Athar Abdul-Quader Purchase College
Title: CP-genericity and neutrality
Abstract: In a paper with Kossak in 2018, we studied the notion of neutrality: a subset X of a model M of PA is called neutral if the definable closure relation in (M, X) coincides with that in M. This notion was suggested by Dolich. motivated by work by Chatzidakis-Pillay on generic expansions of theories. In this talk, we will look at a more direct translation of the Chatzidakis-Pillay notion of genericity, which we call ‘CP-genericity’, and discuss its relation to neutrality. The main result shows that for recursively saturated models, CP-generics are always neutral; previously we had known that not all neutral sets are CP-generic. ​
Information: The seminar will take place virtually. Please email Victoria Gitman (vgitman@nylogic.org) for the meeting id.

CUNY Set Theory Seminar
Time: Friday, August 14, 14:00 New York time (20:00 CEST)
Speaker: Gunter Fuchs CUNY
Title: Canonical fragments of the strong reflection principle
Abstract: I have been working over the past few years on the project of trying to improve our understanding of the forcing axiom for subcomplete forcing. The most compelling feature of this axiom is its consistency with the continuum hypothesis. On the other hand, it captures many of the major consequences of Martin’s Maximum. It is a compelling feature of Martin’s Maximum that many of its consequences filter through Todorcevic’s Strong Reflection Principle SRP. SRP has some consequences that the subcomplete forcing axiom does not have, like the failure of CH and the saturation of the nonstationary ideal. It has been unclear until recently whether there is a version of SRP that relates to the subcomplete forcing axiom as the full SRP relates to Martin’s Maximum, but it turned out that there is: I will detail how to associate in a canonical way to an arbitrary forcing class its corresponding fragment of SRP in such a way that (1) the forcing axiom for the forcing class implies its fragment of SRP, (2) the stationary set preserving fragment of SRP is the full principle SRP, and (3) the subcomplete fragment of SRP implies the major consequences of the subcomplete forcing axiom. I will describe how this association works, describe some hitherto unknown effects of (the subcomplete fragment of) SRP on mutual stationarity, and say a little more about the extent of (3).
Information: Please email Victoria Gitman (vgitman@nylogic.org) for meeting id (this talk will have a different meeting ID!).