The Toronto Set Theory Seminar is normally held on Fridays, from 1:30 to 3pm, in room 210 of the Fields Institute. For listing of talks from years earlier than 2006, see this page.

## Franklin Tall: On the sigma-compactness of definable Menger spaces

Place: Fields Institute (Room 210)

Date: December 2, 2016 (13:30-15:00)

Speaker: Franklin Tall, University of Toronto

Title: On the sigma-compactness of definable Menger spaces

Abstract:  In a previous seminar, we saw that an inaccessible sufficed for the consistency of “every projective Menger set of reals is sigma-compact”. The inaccessible is in fact necessary.

## Juris Steprans: Automorphisms of $P(\omega)/fin$

Place: Fields Institute (Room 210)

Date: November 25th, 2016 (13:30-15:00)

Speaker: Juris Steprans, York University

Title: Automorphisms of $P(\omega)/fin$

Abstract:

The question of whether all automorphisms of $P(\kappa)/fin$ are trivial has been settled in the following cases:

– For $\kappa =\omega$ by Rudin and Shelah
– For $\kappa$ between $\omega_2$ and the first inaccessible by work of Larson & McKenney and Shelah and me.

However the second result hinges on the question for automorphisms of $P(\omega_1)/fin$. I will discuss a resolution to this question stemming from recent work of Shelah and me.

## Haosui Duanmu: Nonstandard analysis and its application to statistical decision theory

Place: Fields Institute (Room 210)

Date: November 18 , 2016 (13:30-15:00)

Speaker: Haosui Duanmu

Title: Nonstandard analysis and its application to statistical decision theory

Abstract: Statistical decision theory has been serving as a rigorous foundation for statistics since its development in the mid 20th century. For statistical decision problem with finite parameter space, every admissible estimator is Bayes which is the well-known complete class theorem. However, such relation begins to break down for general parameter spaces. By using nonstandard analysis, we introduce the notion of hyperfinite statistical decision problem and develop the nonstandard complete class theorem. We show that if there exists a suitable hyperfinite representation of the original statistical decision problem then the nonstandard counterpart of every standard admissible estimator is nonstandard Bayes. We close with a standard complete class theorem for compact parameter spaces.

## Justin Moore: The subgroup structure of Thompson’s group F

Place: Bahen Centre (Room 2179)

Date: November 11, 2016 (15:30- 17:00)

Speaker: Justin Moore, Cornell University

Title: The subgroup structure of Thompson’s group F

Abstract: What is the structure of the finitely generated subgroups of Thompson’s group F, equipped with the embeddability relation? This is conjectured to be a well quasi-order. We prove that it contains a chain of length $\epsilon_0+1$. This is joint work with Matt Brin and Collin Bleak.

## Hossein Lamei Ramandi: A rough classification of non $\sigma$-scattered linear orders

Place: Fields Institute (Room 210)

Date: November 11, 2016 (14:00-15:00)

Title: A rough classification of non $\sigma$-scattered linear orders

Abstract: We prove that under $PFA^+$ every non $\sigma$-scattered linear order contains a real type, an Aronszajn type, or a ladder system indexed by a stationary subset of $\omega_1$ equipped with a lexicographic order or reverse lexicographic order. This is a joint work with Justin Moore.

## Iian Smythe: Generic pure states

Place: Fields Institute (Room 210)

Date: November 11, 2016 (13:00-14:00)

Speaker: Iian Smythe, Cornell University

Title: Generic pure states

Abstract: Using their theory of “quantum filters”, Farah and Weaver showed that a sufficiently generic filter for the projections in the Calkin algebra produces a pathological pure state. In particular, this generic pure state is not pure when restricted to any atomic maximal abelian self adjoint subalgebra, and is thus a counterexample to a conjecture of Anderson. Using Ramsey-theoretic techniques, we give sufficient conditions for filters of projections to yield counterexample to Anderson’s conjecture, and under large cardinal hypotheses, to be generic over the inner model L(R).

## Pedro Sanchez Terraf: Bisimilarity for Probabilistic and Nondeterministic Processes

Place: Fields Institute (Room 210)

Date: November 4th, 2016 (13:30-15:00)

Speaker: Pedro Sanchez Terraf

Title: Bisimilarity for Probabilistic and Nondeterministic Processes

Abstract: Different models of computation have been introduced in Computer Science. Some of these models involve the use of probabilities, and also “non determinism”, that arises when one considers the interaction of processes running in parallel. One of the main concerns is to find appropriate definitions for the intuitive concept of “equivalence of behavior” for processes. A formal version of this notion is given by bisimilarity, the study of which gives rise to a few problems with a descriptive-set-theoretical flavor. In this talk I’ll survey some of these problems.

## Ari Brodsky: More notions of forcing add a Souslin tree

Place: Fields Institute (Room 210)

Date: October 28, 2016 (13:30-15:00)

Speaker: Ari Brodsky, Bar-Ilan University

Title: More notions of forcing add a Souslin tree

Abstract: Shelah proved that Cohen forcing adds an $\omega_1$-Souslin tree. In this work, we identify a rather large class of notions of forcing that, assuming a GCH-type assumption, add a $\lambda^+$-Souslin tree. This class includes Prikry, Magidor and Radin forcing.

This is joint work with Assaf Rinot.

## Franklin Tall: Arhangel’skii’s Lindelof points- $G_{\delta}$ problem

Place: Fields Institute (Room 210)

Date: October 21st, 2016 (13:30-15:00)

Speaker: Franklin Tall

Title: Arhangel’skii’s Lindelof points- $G_{\delta}$ problem

Abstract: My claim of a solution was premature. I will discuss the history of the
problem, introduce n-dowments and the Mitchell collapse, and prove some results that could lead to a solution. If time permits, I will correct and improve a result I talked about last summer, proving that if every Hurewicz projective set of reals in sigma-compact, then there is an inaccessible in an inner model.

## Yinhe Peng: Inner and outer topology for basis problem

Place: Fields Institute (Room 210)

Date: October 7th, 2016 (13:30-15:00)

Speaker: Yinhe Peng

Title: Inner and outer topology for basis problem

Abstract: We will introduce new classes of topological spaces in which the basis problem has a positive answer. We will also see the role that first countability plays.