## Yinhe Peng: PFA implies a class of hereditarily Lindelof spaces are D spaces

Place: Fields Institute (Room 210)

Date: September 22, 2017 (13:30-15:00)

Speaker: Yinhe Peng

Title: PFA implies a class of hereditarily Lindelof spaces are D spaces

Abstract: For a space X, OSM_X asserts that for any open neighbourhood assignment (or open set mapping) N, there is a partition of X into countably many pieces such that for each x, y in the same piece, either x is in N(y) or y is in N(x).

We introduce a property that will force OSM under PFA. We then use OSM to imply D, assuming additional properties (e.g., sub-Sorgenfrey).

## Simon Cho: A Category Theoretic Perspective on Continuous Logic

Thursday, September 21, 2017, from 4 to 5:30pm
East Hall, room 3096

Speaker: Simon Cho (University of Michigan)

Title: A Category Theoretic Perspective on Continuous Logic

Abstract:

Although classical model theory is largely formulated in terms of the framework of sets, there is a rich theory that casts model theoretic structures in a category theoretic setting, a project which began with Lawvere’s thesis on “functorial semantics of algebraic theories” and has since grown into an important subfield of category theory. This interface between classical model theory and category theory continues to be an active area of research today.

In parallel, Lawvere also showed that structures – such as metric spaces – seemingly unrelated to categories arose naturally as examples of categories with appropriate enrichments V (for example V=R in the case of metric spaces). Now continuous logic/metric model theory is a generalization of classical model theory that, roughly, replaces sets with metric spaces and equality with the metric; a natural question to ask is whether the above perspective on metric spaces combines with the way of interpreting classical logic into category theory to produce a way to interpret continuous logic into enriched category theory. This talk will answer this in the affirmative, under reasonable conditions. The talk will make every effort to be self-contained, and as such will assume little to no prior knowledge of category theory.

## Garrett Ervin: The Cube Problem for linear orders

Mathematical logic seminar – Sep 19 2017
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Garrett Ervin
Department of Mathematical Sciences
CMU

Title:     The Cube Problem for linear orders

Abstract:

In the 1950s, Sierpiński asked whether there exists a linear order that is isomorphic to its lexicographically ordered Cartesian cube but not to its square. The analogous question has been answered positively for many different classes of structures, including groups, Boolean algebras, topological spaces, graphs, partial orders, and Banach spaces. However, the answer to Sierpinski’s question turns out to be negative: any linear order that is isomorphic to its cube is already isomorphic to its square, and thus to all of its finite powers. I will present an outline of the proof and give some related results.

## Descriptive Set Theory in Turin, September 6 – 8, 2017

Descriptive Set Theory in Turin Date and place: September 6th to 8th, 2017 – Torino (Italy)

Organizers: Alessandro Andretta, Gianluca Basso, Riccardo Camerlo, Vassilis Gregoriades, Luca Motto Ros and Matteo Viale Location: Department of Mathematics “Giuseppe Peano”, Palazzo Campana, via Carlo Alberto 10, Torino. All talks will take place in Aula A, ground floor. To reach Aula A, enter the building, turn right in the first corridor, at the end which you will turn left. At the end of this corridor turn left again and exit in the courtyard. In front of you is Aula A. Useful information Program Day 1 – Wednesday, September 6 09:00 – Registration 09:30 to 10:20 – Gabriel Debs 10:30 to 11:00 – Coffee Break 11:00 to 11:25 – Dominique Lecomte 11:30 to 11:55 – Miroslav Zeleny 12:00 to 13:30 – Lunch 13:30 – 14:30 Discussion Session: Contributions by Silvia Steila, Yann Pequignot, Itaï Ben Yacoov, and Jean Saint-Raymond. 14:30 to 14:55 – Sy-David Friedman 15:00 to 15:50 – Forte Shinko 16:00 to 16:30 – Coffee Break 16:30 to 16:55 – Maciej Malicki 17:00 to 17:25 – Philipp Schlicht Day 2 – Thursday, September 7 09:00 to 09:50 – Julien Melleray 10:00 to 10:25 – Mirna Dzamonja 10:30 to 11:00 – Coffee Break 11:00 to 11:25 – Donát Nagy 11:30 to 11:55 – Márk Poór 12:00 to 13:30 – Lunch 13:30 – 14:30 Discussion Session: Contributions by Dorottya Sziraki, Riccardo Camerlo, Louis Vuilleumier, and Petr Holicky. 14:30 to 14:55 – Jacques Duparc 15:00 to 15:25 – Vladimir Kanovei 15:30 to 15:55 – Pandelis Dodos 16:00 to 16:30 – Coffee Break 16:30 to 16:55 – Raphael Carroy 17:00 to 17:25 – Lionel Nguyen Van Thé Day 3 – Friday, September 8 09:00 to 09:50 – Stephen Jackson 10:00 to 10:25 – Michal Doucha 10:30 to 11:00 – Coffee Break 11:00 to 11:25 – Vojta Kovarik 11:30 to 11:55 – Filippo Calderoni 12:00 to 13:30 – Lunch 13:30 – 14:30 Discussion Session: Contributions by Filippo Cavallari, Vibeke Quorning, Giorgio Laguzzi, and Andrea Vaccaro. 14:30 to 14:55 – Asger Tornquist 15:00 to 15:25 – David Schrittesser 16:00 – Coffee and farewell

Registered Participants

1. Alessandro Andretta, Università di Torino.
2. Gianluca Basso, Université de Lausanne and Università di Torino.
3. Itaï Ben Yaacov, Université Claude Bernard Lyon 1.
4. Filippo Calderoni, Università di Torino.
5. Riccardo Camerlo, Polytechnic of Turin.
6. Raphael Carroy, Kurt Gödel Research Center.
7. Filippo Cavallari, University of Turin, University of Lausanne.
8. Gabriel Debs, Institut Mathématique de Jussieu.
9. Pandelis Dodos, Department of Mathematics, University of Athens.
10. Michal Doucha, Institute of Mathematics, Czech Academy of Sciences.
11. Jacques Duparc, University of Lausanne.
12. Mirna Dzamonja, University of East Anglia.
13. Sy-David Friedman, Kurt Gödel Research Center, U.Vienna.
14. Vassilios Gregoriades, University of Turin.
15. Petr Holicky, Charles University, Prague.
16. Stephen Jackson, University of North Texas.
17. Vladimir Kanovei, Institute for the Information Transmission Problems.
18. Vojta Kovarik, Charles University, Prague.
19. Giorgio Laguzzi, University of Freiburg.
20. Dominique Lecomte, Université Pierre et Marie Curie.
21. Maciej Malicki, Warsaw School of Economics.
22. Julien Melleray, Université Lyon 1.
23. Luca Motto Ros, University of Turin.
24. Donát Nagy, Eötvös Loránd University, Budapest.
25. Lionel Nguyen Van Thé, Aix-Marseille University.
26. Yann Pequignot, University of California, Los Angeles.
27. Márk Poór, Eötvös University, Budapest.
28. Vibeke Quorning, University of Copenhagen.
29. Jean Saint Raymond, Université Pierre et Marie Curie – Paris 6.
30. Philipp Schlicht, University of Bonn.
31. David Schrittesser, Kurt Gödel Research Center.
32. Forte Shinko, McGill University.
33. Silvia Steila, University of Bern.
34. Dorottya Sziraki, Alfred Renyi Institute of Mathematics, and Central European University.
35. Asger Tornquist, University of Copenhagen.
36. Andrea Vaccaro, Università di Pisa – York University.
37. Matteo Viale, Università di Torino.
38. Louis Vuilleumier, Université de Lausanne.
39. Domenico Zambella, Università di Torino.
40. Miroslav Zeleny, Faculty of mathematics and physics, Charles University, Prague, Czech Republic.

Sponsors The workshop is generously funded by – The Department of mathematics “Giuseppe Peano” – Programma Giovani Ricercatori “Rita Levi Montalcini”, “Nuovi sviluppi in teoria descrittiva degli insiemi”, (PI:Luca Motto Ros) – PRIN 2012 “Modelli e insiemi” (PI: Carlo Toffalori)

## Marcos Mazari Armida: Introduction to good frames in Abstract Elementary Classes

Hello,

The seminar will continue to meet on Mondays in WeH 8201 at 5PM, the talks usually last 90 minutes.
Marcos Mazari Armida will give at least three talks, introducing Shelah’s good frames which the generalization to Abstract Elementary Classes of forking, he will focus on obtaining exists theorem of models when model theoretic assumptions will be replacing rather article non-ZFC axioms used by Shelah.
Information on this seminar is posted on the departmental web page http://www.math.cmu.edu/math/modeltheoryseminars/modeltheoryseminar.php?SeminarSelect=1548  or see below.
Best,
Rami Grossberg.
——————————————————-

Marcos Mazari Armida

Carnegie Melllon University
Title: Introduction to good frames in Abstract Elementary Classes, Part 1

Abstract:
The central notion of Shelah’s book on Abstract Elementary Classes [Sh:h] is the notion of a good $\lambda$-frame. It is a forking like notion for types over models of size $\lambda$ and the existence of it implies that the class is well-behaved in $\lambda$. In this series of talks we will focus on the question of the existence of extensions to models of size greater than $\lambda$. We will prove that under some reasonable hypothesis it is always possible to extend a frame. One interesting corollary of this is the existence of arbitrary large models, this is done within ZFC. The first couple of lectures will be based on [Sh:h] Chapter II, while our main theorem is the main theorem of [Bon14a].

References:
[Bon14a] Will Boney, Tameness and extending frames, Journal of Mathematical Logic 14, no. 2
[Sh:h] Saharon Shelah, Classication Theory for Abstract Elementary Classes, vol. 1 & 2, Mathematical Logic and Foundations, no. 18 & 20, College Publications, 2009.

Date: Monday , September 18, 2017.
Time: 5:00 pm
Location: Wean Hall 8201

Marcos Mazari Armida

Carnegie Melllon University
Title: Introduction to good frames in Abstract Elementary Classes, Part 2

Abstract:
The central notion of Shelah’s book on Abstract Elementary Classes [Sh:h] is the notion of a good $\lambda$-frame. It is a forking like notion for types over models of size $\lambda$ and the existence of it implies that the class is well-behaved in $\lambda$. In this series of talks we will focus on the question of the existence of extensions to models of size greater than $\lambda$. We will prove that under some reasonable hypothesis it is always possible to extend a frame. One interesting corollary of this is the existence of arbitrary large models, this is done within ZFC. The first couple of lectures will be based on [Sh:h] Chapter II, while our main theorem is the main theorem of [Bon14a].

References:
[Bon14a] Will Boney, Tameness and extending frames, Journal of Mathematical Logic 14, no. 2
[Sh:h] Saharon Shelah, Classication Theory for Abstract Elementary Classes, vol. 1 & 2, Mathematical Logic and Foundations, no. 18 & 20, College Publications, 2009.

Date: Monday , September 25, 2017.
Time: 5:00 pm
Location: Wean Hall 8201

Marcos Mazari Armida

Carnegie Melllon University
Title: Introduction to good frames in Abstract Elementary Classes, Part 3

Abstract:
The central notion of Shelah’s book on Abstract Elementary Classes [Sh:h] is the notion of a good $\lambda$-frame. It is a forking like notion for types over models of size $\lambda$ and the existence of it implies that the class is well-behaved in $\lambda$. In this series of talks we will focus on the question of the existence of extensions to models of size greater than $\lambda$. We will prove that under some reasonable hypothesis it is always possible to extend a frame. One interesting corollary of this is the existence of arbitrary large models, this is done within ZFC. The first couple of lectures will be based on [Sh:h] Chapter II, while our main theorem is the main theorem of [Bon14a].

References:
[Bon14a] Will Boney, Tameness and extending frames, Journal of Mathematical Logic 14, no. 2
[Sh:h] Saharon Shelah, Classication Theory for Abstract Elementary Classes, vol. 1 & 2, Mathematical Logic and Foundations, no. 18 & 20, College Publications, 2009.

Date: Monday , October 2, 2017.
Time: 5:00 pm
Location: Wean Hall 8201

## Yuan Yuan Zheng: Moderately-abstract parametrized Ellentuck theorem

Place: Fields Institute (Room 210)

Date: September 15, 2017 (13:30-15:00)

Speaker: Yuan Yuan Zheng

Title: Moderately-abstract parametrized Ellentuck theorem

Abstract: Mimicking the parametrized Ellentuck theorem in the Ellentuck
space and the parametrized Milliken theorem in the Milliken space, we
present a ‘moderately abstract’ parametrized theorem for ‘moderate’
topological Ramsey spaces. It is a parametrization of the abstract
Ellentuck theorem with infinitely many perfect sets of real numbers,
implying that essentially all infinitely-dimensional Ramsey properties
proven using topological Ramsey space theory can be parametrized by
products of infinitely many perfect sets.

## On the Infinite, Paris, October 18 – 21, 2017

On the Infinite

An Interdisciplinary Symposium

October 18 – October 21, 2017

Infinity: the break in the horizon, the “what cannot be counted”, boundless, bottomless, eternal, illimitable and absolute. The infinite encloses physical space; the infinite holds time within itself.

Already in the classical period, philosophers were undone by Zeno’s paradox, that an arrow shot from its bow will never reach its target because it must pass through every point between bow and target, and there are infinitely many such points. For cosmologists, the urgent question is: Is the universe finite or infinite? Will it last forever? And theologians saw in it an attribute of God, and were even prohibited to talk about it.

For the mathematician the infinite is the oil in the machine. For the mathematician who is a set theorist the infinite is a totality—completed, though in Aristotle’s sense, out of view; while at the same time the infinite is essentially open: open “above”, so numberless; but also open inwardly, in the way it copies itself internally over and over again, prints an image of itself into every one of its proper parts, and reprints, and reprints, and reprints, toward an endlessly fractured and ramified whole.

Critical conceptions of the infinite coming from outside of mathematics may coalesce around the concept of seriality. In The Infinite Line the art historian Briony Fer writes of the various serial strategies available to the artist; how “repetition, splintered into multiple registers, [is] no longer pitched against the aura of a single, unique artwork, so much as against its other selves.”

In this four-day interdisciplinary symposium we juxtapose lectures by set theorists and other mathematicians with those by art historians, architects, artists and philosophers, in an attempt to create a dialogue across cultures.

Some of the mathematical talks will be aimed at a general audience.

The symposium is accompanied by an exhibition of the work of the sculptor Fred Sandback.

Invited Speakers:

• Yves André (mathematics, Paris VI)
• Andrew Arana (philosophy, IHPST Paris)
• Joan Bagaria (mathematics, Barcelona)
• Maria Clara Cortés (art, Universidad Nacional de Colombia)
• Briony Fer (art history, UCL)
• Sebastian Gandon (philosophy, Clermont-Ferrand)
• Wilfrid Hodges (mathematics, QML emeritus)
• Hanna Johansson (art history, Helsinki)
• Menachem Magidor (mathematics, Hebrew University)
• Maryanthe Malliaris (mathematics, University of Chicago)
• Philip Ording (mathematics, Sarah Lawrence College)
• Juhani Pallasmaa (architecture, Helsinki)
• Marja Sakari (art history, Kiasma, Helsinki)
• SMITH (artist, Paris)
• John Steel (mathematics, Berkeley)
• Valdimir Tasic (mathematics, University of New Brunswick)
• Jean-Philippe Uzan (CNRS, Institut d’Astrophysique de Paris)
• Andres Villaveces (mathematics, Bogotá)
• Philip Welch (mathematics, Bristol)
• Hugh Woodin (mathematics and philosophy, Harvard)

Exhibition: Fred Sandback at the Institute Henri Poincaré.

Organizers:

Michael Harris, Columbia University, New York
Juliette Kennedy, University of Helsinki
Boban Velickovic, Paris Diderot University

Finnish Academy of Science and Letters
Institute Français de Finland
University of Helsinki
Institute Henri Poincaré
European Research Council
Magnus Ehrnrooth Foundation

## Set Theory, Model Theory and Applications (In memory of Mati Rubin), Eilat, April 22-26, 2018

RESEARCH WORKSHOP OF THE ISRAEL SCIENCE FOUNDATION

Set Theory, Model Theory and Applications

(In memory of Mati Rubin)

The international conference Set Theory, Model Theory and Applications,in memory of our late colleague Mati Rubin, will take place at the Eilat Campus of Ben-Gurion University of the Negev (Israel) from 22 – 26 April, 2018.

Eilat is Israel’s southernmost city, a popular resort located at the northern tip of the Red Sea, on the Gulf of Eilat. The following Eilat Official Tourism Site contains a lot of useful information.

The main purpose of the conference is to bring together mathematicians working in the areas of set theory and model theory in which Mati Rubin worked in order to exchange ideas and present results of current research.

The total expected number of participants is 70. The list of confirmed participants may be found in here.

Depending on the number of participants we may have some lectures in parallel.

There is no Conference registration fee.

Accommodation: The Organizing Committee will book the rooms for all participants in the Hotel Adi and will offer special prices in this hotel. Eilat has plenty of hotels and in principal the participants could book a hotel of their choice on their own.

Travel to Eilat: Arkia and Israir are the airlines operating flights from TLV (Ben-Gurion international airport)  to Eilat.

We are planning to have Conference Dinner and an excursion for the conference participants and accompanying persons.

Possible financial support depends on the total funds that we shall be able to obtain.

Scientific Committee:

• Uri Abraham (Ben-Gurion University),
• Assaf Hasson (Ben-Gurion University),
• Menachem Kojman (Ben-Gurion University)

Organizing Committee:

Workshop sponsored by the Israel Science Foundation and the Center for Advanced Studies in Mathematics, BGU, Beer Sheva, Israel

Additional support by BGU President, Rector and Dean of the Faculty of Natural Sciences

## Miha Habič: The grounded Martin’s axiom

Dear all,

The seminar meets on Wednesday September 13th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Miha Habič — The grounded Martin’s axiom

We will examine the notion of a grounded forcing axiom, which asserts
that the universe is a forcing extension by a forcing notion from a
particular class and that the usual forcing axiom holds for forcings
from that class coming from the ground model of the extension. We shall
focus in particular on the grounded Martin’s axiom, where the universe
is a ccc extension. The principle has some of the combinatorial strength
of MA, but allows for more flexibility (for example, a singular
continuum). Furthermore, it is more robust under mild forcing extensions
than full MA, since it is often preserved after adding a Cohen or a
random real. We will also briefly glance at grounded versions of other
forcing axioms, such as grounded PFA, and outline some open questions in
the area.

Best,
David

## Micheal Pawliuk: The Perfect Expansion Property

Place: Fields Institute (Room 210)

Date: September 8, 2017 (13:30-15:00)

Speaker: Micheal Pawliuk

Title: The Perfect Expansion Property

Abstract: The expansion property for classes of finite structures is a well studied Ramsey property for homogeneous structures. Recently, a quantitative version of this property was introduced to answer questions related to amenability and unique ergodicity of automorphism groups of homogeneous structures. A typical way to check this property involves fine estimates and the probabilistic method.

We introduce an even stronger expansion property that is purely combinatorial, while not being so strong as to be impossible. We will then classify which completely n-partite directed graphs have this property. Remarkably, the property is able to isolate the geometry of completely n-partite directed graphs.

This provides a step in the right direction towards the goal of showing that the semigeneric digraph has a uniquely ergodic automorphism group (which is still open).