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.

## 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.

## Zoltan Vidnyanszky: Characterization of order types representable by Baire class 1 functions

Place: Fields Institute (Room 210)

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

Speaker: Zoltan, Vidnyanszky, York University

Title: Characterization of order types representable by Baire class 1 functions

Abstract: Let $\mathcal{F}$ be a family of real valued functions on a Polish space $X$. A natural partial ordering on $\mathcal{F}$ is the pointwise ordering, $\leq_p$. The description of linearly ordered subsets of $(\mathcal{F},\leq_p)$ reveals a lot of information about the poset itself. It turns out that the first interesting family of functions to consider is the family of Baire class 1 functions, $\mathcal{B}_1(X)$. Answering a question of Laczkovich, we give a complete combinatorial characterization of the linearly ordered subsets of $(\mathcal{B}_1(X),\leq_p)$.

## Franklin Tall: Work in progress

Place: Fields Institute (Room 210)

Date: September 23, 2016 (13:30-15:00)

Speaker: Franklin Tall, University of Toronto

Title: Work in progress

Abstract: Depending on what I accomplish in the next week, I will either speak on the cardinality of regular Lindelof spaces with points $G_{\delta}$ or else on some connections among spaces satisfying the Baire Category Theorem, logics satisfying the Omitting Types Theorem, and non-meager P-filters.

## Ian Greig: Dense Subsets of $2^c$ and Independent Families

Place: Fields Institute (Room 210)

Date: September 9th, 2016 (13:30-15:00)

Speaker: Ian Greig

Title: Dense Subsets of $2^c$ and Independent Families

Abstract: We examine the topological space of all functions from the continuum into 2. Specifically, we show that there exists a countable dense subset of this space such that no point in the space is the limit of a sequence from our dense set. Additionally, under the assumption of Martin’s Axiom for Countable Partial Orders, we construct a countable dense subset D such that any discrete subset of D is closed.

## Ashutosh Kumar: Avoiding rational distances in plane

Place: Bahen Centre (Room BA 2135)

Date: August 26th, 2016 (13:30-15:00)

Speaker: Ashutosh Kumar

Title: Avoiding rational distances in plane

Abstract: We show that every graph of countable coloring number on a set of reals has an everywhere non meager independent set. In particular, every set of points in the plane has an everywhere non meager subset no two of whose points are at a rational distance.

## Secil Tokgoz: OCA and Menger’s Conjecture

Place: Bahen Centre (Room BA2135)

Date: August 19th , 2016 (13:30-15:00)

Speaker: Secil Tokgoz

Title: OCA and Menger’s Conjecture

Abstract: It was previously known that Projective Determinacy implies Menger projective sets of reals are sigma-compact. The hypothesis has considerable large cardinal strength; we are able to reduce the conclusion’s consistency strength to that of an inaccessible. In fact this is an equiconsistency result. We derive the conclusion from a perfect strengthening of OCA. Equiconsistency is proved by an argument involving the dominating number and the Covering Lemma. This is joint work by Secil Tokgoz, Frank Tall and S. Todorcevic.

## Miguel Angel Mota: Measuring together with the continuum large

Place: TBD

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

Speaker: Miguel Angel Mota

Title: Measuring together with the continuum large

Abstract:  Measuring, as defined by Justin Moore, says that for every sequence $(C(\delta))_{\delta<\omega_1}$ with each $C(\delta)$ being a closed subset of $\delta$ there is a club $C\subseteq\omega_1$ such that for every $\delta \in C$, a tail of $C\cap\delta$ is either contained in or disjoint from $C(\delta)$. We answer a question of Justin Moore by building a forcing extension satisfying measuring together with $2^{\aleph_0}>\aleph_2$.

## Ilijas Farah: A consistent failure Glimm’s theorem for nonseparable C*-algebras

Place: Fields Institute (Room 210)

Date: June 24th, 2016 (13:30-15:00)

Speaker: Ilijas Farah

Title: A consistent failure Glimm’s theorem for nonseparable C*-algebras

Abstract: A remarkable 1960 result of J. Glimm provides a sharp dichotomy for
the representation theory of separable C*-algebras. One of its
consequences is that a separable C*-algebra either has a unique
(up to the unitary equivalence) irreducible representation or continuum
many inequivalent irreducible representations. Using some ideas of
Akemann and Weaver, I’ll prove that this conclusion is consistently false
for nonseparable C*-algebras. Many open problems remain.

## David Fernández Bretón: Ultrafilters on the rationals generated by perfect sets

Place: Fields Institute (Room 210)

Date: June 17th, 2016 (13:30-15:00)

Speaker: David Fernandez Bretón

Title: Ultrafilters on the rationals generated by perfect sets

Abstract:  In a 1992 paper, van Douwen defined what he calls a
“gruff ultrafilter”: an ultrafilter on the rational numbers which
is generated by perfect (this is, closed and crowded) sets; and
asked whether these ultrafilters exist, providing in the same
paper a proof that they do if cov(M)=c. The question of whether
the existence of gruff ultrafilters can be proved in ZFC alone
remains open, but further progress has been made in the
way of consistently positive answers. In this talk I will
present a proof that gruff ultrafilters exist in the Random
model, as well as in any model satisfying d=c. Joint work
with Michael Hrusak.

## Dana Bartosova: Algebra in the Samuel compactification

Place: Fields Institute (Room 210)

Date: June 10, 2016 (13:30-15:00)

Speaker: Dana Bartosova

Title: Algebra in the Samuel compactification

Abstract: The Samuel compactification, or the greatest ambit, is an important compactification of a topological group for its dynamics. In the case of discrete groups, the Samuel compactification coincides with the Cech-Stone compactification and its algebra and combinatorics have been extensively studied. We remind the Samuel compactification for automorphism groups in the ultrafilter language and point out some differences and similarities with the discrete case. We will then apply algebra and combinatorics to answer a problem of Ellis for the group of permutations of the integers. This is a joint work in progress with Andy Zucker (Carnegie Mellon University).