## Alessandro Vignati: Set theoretical dichotomies in the theory of continuous quotients

Place: Fields Institute (Room 210)

Date: April 28, 2017 (13:30-15:00)

Speaker: Alessandro Vignati, York University

Title: Set theoretical dichotomies in the theory of continuous quotients

Abstract: We state and (depending on time) prove some dichotomies of set theoretical nature arising in the theory of continuous quotients. In particular we show that the assumption of CH on one side, and of Forcing Axioms on the other, affects the nature of possible embeddings of certain corona algebras, as well as the behavior of their automorphisms group. This is partly joint work with P. McKenney.

## Set theoretic & Topological methods in Model Theory, Tezpur, September 7–12, 2017

The aim of this programme is to bring together mathematicians and logicians working on/interested in various topics on the border of model theory, topology and set theory. The leading themes are topological dynamics and descriptive set theoretic methods in model theory. Apart from the state of the art lectures by leading experts, two tutorials, each consisting of 3 one-hour talks on the main themes of the meeting, are being planned. The meeting will give opportunity for discussion and collaboration between experts from different but related parts of logic. This may result in the future in discovering new interactions between model theory, topology and set theory.

There is no conference fee. However, all invited speakers and participants must register. Accommodation and food for all participants will be provided by the guest house of Tezpur University. Check in date at the guest house is 6th september, 2017 and check out is 13th september, 2017.

# Invited Speakers

• Ehud Hrushovski, Oxford.
• Tomás Ibarlucía, Paris.
• Byunghan Kim, Yonsei.
• Aleksandra Kwiatkowska, Münster, Germany.
• Ludomir Newelski, Wrocław.
• Julien Melleray, Lyon.
• Anand Pillay, Notre Dame.
• Nick Ramsey, Berkeley.
• Tomasz Rzepecki, Wrocław.
• Slawomir Solecki, Urbana–Champaign.
• Charles Steinhorn, Vassar College, New York.
• Todor Tsankov, Paris.
• Frank Wagner, Lyon.

# Tutorials

• Artem Chernikov
• Krzysztof Krupiński

## Alberto Marcone: Some results about the higher levels of the Weihrauch lattice

KGRC Research Seminar – 2017‑04‑27 at 4pm

Speaker: Alberto Marcone (Università di Udine, Italy)

Abstract: In the last few years Weihrauch reducibility and the ensuing Weihrauch lattice have emerged as a useful tool for studying the complexity of mathematical statements viewed as “problems” or multi-valued functions. This approach complements nicely the reverse mathematics approach, and has been very successful for statements which are provable in ${\mathsf{ACA}_0}$. The study the Weihrauch lattice for functions arising from statements laying at higher levels, such as ${\mathsf{ATR}_0}$, of the reverse mathematics spectrum is instead in its infancy. We will present some results (work in
progress with my graduate student Andrea Cettolo).

In some cases we obtain the expected finer classification, but in other we observe a collapse of statements that are not equivalent with respect to provability in subsystems of second order arithmetic. This is in part due to the increased syntactic complexity of the statements. Our preliminary results deal with comparability of well-orderings, $\Sigma^1_1$-separation, and
$\Delta^1_1$-comprehension.

## 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