## Matteo Viale: Useful axioms

KGRC Research Seminar – 2017‑04‑26 at 4pm

Speaker: Matteo Viale (Università di Torino, Italy)

Abstract: ￼I overview several aspects of forcing axioms which (in my eyes) give solid mathematical arguments explaining why these axioms are so useful in establishing new (consistency) results and/or theorems.

• The first aspect outlines that forcing axioms are natural strengthenings not only of Baire’s category theorem, but also of the axiom of choice (these are two of the most useful non-constructive principles in mathematics), and also strengthenings of most large cardinal axioms (at least for cofinally many of them).
• The second aspect outlines that Shoenfield’s absoluteness, Cohen’s forcing theorem, and Los theorem for standard ultrapowers of a first order structure by a non principal ultrafilter are all specific instances of a more general form of Los theorem which can be declined for what I call boolean ultrapowers.
• The third aspect outlines how strong forcing axioms and Woodin’s generic absoluteness results are two sides of the same coin and will try to explain how stronger and stronger forms of generic absoluteness can be obtained by asserting stronger and stronger forcing axioms. In this context category theoretic ideas start to play a role and we are led to analyze forcings whose conditions are (certain classes of) forcing notions and whose order relation is given by (certain classes of) complete embeddings.

There is a surprising analogy between the theory of these class forcings, the theory of towers of normal ideals, and many of the classical arguments yielding generic absoluteness results. For what concerns the first two aspects of my talk, I do not claim authorship of essentially none of the result I will be talking about, nonetheless it is hard to attribute correctly the relevant results.

## Nicholas Ramsey: NSOP_1 Theories

BGU seminar in Logic, Set Theory and Topology.

Time: Tuesday, April 25th, 12:15-13:30.
Place: Seminar room -101, Math building 58.
Speaker: Nicholas Ramsey (UC Berkeley)

Title: NSOP_1 Theories

Abstract:
The class of NSOP_1 theories was isolated by Džamonja and Shelah in the mid-90s and later investigated by Shelah and Usvyatsov, but the theorems about this class were mainly restricted to its syntactic properties and the model-theoretic general consensus was that the property SOP_1 was more of an unimportant curiosity than a meaningful dividing line. I’ll describe recent work with Itay Kaplan which upends this view, characterizing NSOP_1 theories in terms of an independence relation called Kim-independence, which generalizes non-forking independence in simple theories.  I’ll describe the basic theory and describe several examples of non-simple NSOP_1 theories, such as Frobenius fields and vector spaces with a generic bilinear form.

## Marcin Michalski: Luzin’s theorem

Tuesday, April 25, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Marcin Michalski (Wroclaw University of Science and Technology)

Title: Luzin’s theorem

Abstract:

In 1934 Nicolai Luzin proved that each subset of the real line can be decomposed into two full subsets with respect to ideal of measure or category. We shall present the proof of this result partially decoding his work and we will also briefly discuss possible generalizations.

## Applications of model theory to operator algebras, Houston, July 31 – August 4

Dear Colleagues,

This is an announcement for an NSF-funded conference on “Applications
of Model Theory to Operator Algebras” to be held at the University of
Houston from July 31 — August 4, 2017. This conference will feature a
lecture series by our main speaker, Ilijas Farah, as well as several
plenary research talks by various experts in Operator Algebras and
Model Theory.

https://www.math.uh.edu/analysis/2017conference.html

The purpose of this conference is two-fold: First, to serve as a
“master class” for non-experts and young researchers to learn about
fundamental concepts presented by Professor Ilijas Farah, a leading
expert and renowned expositor of these topics; and second, to inform
and update experts in other areas of operator algebras about the
these talks, and the topics covered, can be found on the conference
website.

We hope you will be able to attend.

Sincerely,

The Organizers
Mark Tomforde (University of Houston)
Ping Wong Ng (University of Louisiana at Lafayette)
Leonel Robert (University of Louisiana at Lafayette)

## Ari Brodsky: Distributive Aronszajn trees

Place: Fields Institute (Room 210)

Date: April 21, 2017 (13:30-15:00)

Speaker: Ari Brodsky, Bar-Ilan University

Title: Distributive Aronszajn trees

Abstract: We address a conjecture asserting that, assuming GCH, for every singular cardinal $\lambda$, if there exists a $\lambda^+$-Aronszajn tree, then there exists one which is moreover $\lambda$-distributive.A major component of this work is the study of postprocessing functions and their effect on square sequences. This is joint work with Assaf Rinot

## Andrés Caicedo: Real-valued measurability and Lebesgue measurable sets

University of Notre Dame, Logic Seminar • 125 Hayes-Healy Hall
Tue May 2, 2017 2:00PM – 3:00PM

Speaker: Andres Caicedo – Mathematical Reviews

Title: Real-valued measurability and Lebesgue measurable sets

Abstract: I will show that the existence of atomlessly measurable cardinals does not settle the range of Lebesgue measure on the projective sets.

## The 15th Asian Logic Conference, Korea, July 10–14, 2017

The Fifteenth Asian Logic Conference will be held in Daejeon, Korea during July 10 – 14, 2017. It will be the first Asian Logic Conference since its status changed from an ASL(the Association for Symbolic Logic)-sponsored meeting to an official ASL meeting by ASL Council action in May 2016.

The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields in mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere to exchange information and ideas.

From 1981 to 2008, the Asian Logic Conference has been held triennially and rotated among countries in the Asia-Pacific region. The previous meetings took place in Singapore (1981), Bangkok (1984), Beijing (1987), Tokyo (1990), Singapore (1993), Beijing (1996), Hsi-Tou (1999), Chongqing (2002), Novosibirsk (2005), and Kobe (2008). In 2008, the East Asian and Australasian Committees of the Association for Symbolic Logic decided to shorten the three-year cycle to two. The new two-year cycle began with the meeting in Singapore (2009), and subsequent meetings have been held in Wellington (2011), Guangzhou (2013), and Mumbai (2015).

Some of the previous meetings’ websites can be found HERE.

## Plenary Speakers

• Johann Makowsky (Technion IIT, Israel)
•  Sara Negri (University of Helsinki, Finland)
•  Yinhe Peng (University of Toronto, Canada)
•  Katrin Tent (University of Münster, Germany)
•  Kwangkeun Yi (Seoul National University, Korea)
•  Yimu Yin (Sun Yat-sen University, China)
•  Liang Yu (Nanjing University, China)
•  Yizheng Zhu (University of Münster, Germany)

## Special Session in ​Set Theory

• Yurii Khomskii (University of Hamburg, Germany)
• Paul Larson (Miami University, USA)
• Diego Mejía (Shizuoka University, Japan)
• Hiroshi Sakai (Kobe University, Japan)

## ​

May 12, 2017 : Deadline for contributed talk applications.

May 29, 2017 :

• Deadline for the payment of reduced registration fee by bank transfer. (After this date, registration fee will no longer be accepted by bank transfer. Only on-site payment (in cash) of standard registration fee will be accepted during the first day of conference.)

• Notification of the result of contributed talk applications.

June 30, 2017 (or when there are 120 registered participants before this date) : Registration closes.

July 10 – 14, 2017 : Conference

## Classification problems in ergodic theory, Irvine, July 14–25, 2017

A 2-week summer school will take place at UC Irvine from Aug. 14 – 25, 2017. The topic of the school will be classification problems in ergodic theory. Lectures will be given by Peter Burton, Matt Foreman, and Brandon Seward.
1. The first week will treat positive classification results and associated tools. We will primarily focus on entropy theory, starting with the classical entropy theory for actions of countable amenable groups and ending with the quite recent developments of entropy theory for actions of countable non-amenable groups (in particular sofic groups).
2. The second week will be concerned with anti-classification results: results showing that classifications are not possible with countable resources. We begin with a review of naive descriptive set theory and then discuss classification in this framework. We proceed to show that the classification problem is not solvable for Z-actions, even of real analytic diffeomorphisms of the torus. Finally, we place the classification problems in the hierarchy of analytic equivalence relations under Borel reducibility.
The deadline for applications is May 15, however late applications will still be considered on a case-by-case basis. Funding is available for US citizens and permanent residents (per grant restrictions). More information can be found here:

## Borel Reducibility of Equivalence Relations, Lausanne, May 29, 2017

SGSLPS 2017 Spring meeting on “Borel Reducibility of Equivalence Relations”

Université de Lausanne (Unil), Amphipôle, Room 340

29 May 2017, 10:30 – 17:00

The SGSLPS 2017 Spring meeting on “Borel Reducibility of Equivalence Relations” will feature four hour-long talks by leading experts in the field. The first talk will be introductory and will aim at a general audience.

Speakers:

•  Andrew Brooke-Taylor (University of Leeds, Leeds)
• Raphaël Carroy (Kurt Gödel Research Centre, Vienna)
• Julien Melleray (Université Claude Bernard Lyon 1, Lyon)
• Luca Motto Ros (Università di Torino, Turin
Classification has always been a central theme in mathematics. The study of Borel Reducibility of Equivalence Relations deals with the classification of points of standard Borel spaces up to equivalence relations by explicit, or Borel, mappings between such spaces.

This idea gives rise to a notion of complexity of equivalence relations, and tools from Descriptive Set Theory are used to compare such relations and measure their complexities.

Organisers:
The SGSLPS 2017 Spring meeting is organised by the Swiss Graduate Society for Logic and Philosophy of Science, SGSLPS, with funding by the Swiss Academy of Sciences.
The Swiss Graduate Society for Logic and Philosophy of Science (SGSLPS) is an association of advanced undergraduate and graduate students with a distinctive interest in the large domains of logic and philosophy of science

## James Cummings: Definable subsets of singular cardinals

Mathematical logic seminar – Apr 11 2017
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         James Cummings
Department of Mathematical Sciences
CMU

Title:     Definable subsets of singular cardinals

Abstract:

Shelah proved the surprising result that if μ is a singular strong limit cardinal of uncountable cofinality, then there is a subset X of μ such that all subsets of μ are ordinal-definable from X. We will give a proof and discuss some complementary consistency results.