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.

## Jordi Lopez-Abad: Approximate Ramsey property of matrices and f.d. normed spaces

Place: Fields Institute (Room 210)

Date: November 20th , 2015 (13:00-14:00)

Title: Approximate Ramsey property of matrices and f.d. normed spaces

Abstract: We present the approximate Ramsey property  of  the finite dimensional normed spaces. This is a particular case of a result concerning “metric Ramsey degrees” of matrices. This is a joint work with D. Bartosova and B. Mbombo (U. Sao Paulo)

## Julien Melleray: The simplex of invariant measures of a minimal homeomorphism

Place: Fields Institute (Room 210)

Date: November 20th, 2015 (14:00-15:00)

Speaker: Julien Melleray

Title: The simplex of invariant measures of a minimal homeomorphism

Abstract:  (joint work with Tomás Ibarlucia) We give a characterization
of all simplices of probability measures on a Cantor space X which may
be realized as the simplex of all invariant probability measures for
some minimal homeomorphism g of X. This extends a result of Akin for the
case when K is a singleton, and an unpublished result of Dahl when K is
finite-dimensional. All relevant notions of topological dynamics will be
recalled.

## Chris Eagle: Definability in infinitary [0, 1]-valued logic

Place: Fields Institute (Room 210)

Date: November 13th, 2015 (13:30-15:00)

Speaker: Chris Eagle

Title: Definability in infinitary [0, 1]-valued logic

Abstract: In recent years there have been several proposals for the
“right” analogue of the infinitary logic $L_{\omega_1, \omega}$ for metric
structures.  I will present the three most recent candidates, and discuss
issues around definablity in each of those logics.  The main result is
that in the most expressive of these logics, a continuous [0, 1]-valued
function on a complete separable metric structure is definable if and only
if it is automorphism invariant.

## Yinhe Peng: Higher finite powers of L spaces and higher dimensions of combinatorial properties

Place: Fields Institute (Room 210)

Date: November 6th, 2015 (13:30-15:00)

Speaker: Yinhe Peng

Title: Higher finite powers of L spaces and higher dimensions of combinatorial properties

Abstract: We will see examples of L spaces whose square (or even some higher power) is still an L space (in a joint paper with Liuzhen). We will then see the combinatorial properties behind this and their dimensions.

## Dimitris Vlitas: An infinite self dual Ramsey theorem

Place: Fields Institute (Room 210)

Date: October 30th, 2015 (13:30-15:00)

Speaker: Dimitris Vlitas

Title: An infinite self dual Ramsey theorem

Abstract: We extend the classical infinite Ramsey and the Carlson-Simpson theorem simultaneously to obtain an infinite self dual Ramsey theorem. As a consequence we introduce a new family of Ramsey topological spaces.

## Ashutosh Kumar: A transversal of full outer measure

Place: Fields Institute (Room 210)

Date: October 16th, 2015 (13:30-15:00) and October 23rd, 2015 (13:30-15:00)

Speaker: Ashutosh Kumar

Title: A transversal of full outer measure

Abstract: For every partition of a set of reals into countable sets, there is a transversal of same outer measure. Joint work with Shelah.

## Jose Iovino: Model Theory and the Mean Ergodic Theorem

Place: Fields Institute (Room 210)

Date: October 9th , 2015 (13:30-15:00)

Speaker: Jose Iovino

Title: Model Theory and the Mean Ergodic Theorem

Abstract: I will discuss some recent generalizations of Von Neumann’s mean ergodic theory and their connection with standard model-theoretic ideas.

## Yinhe Peng: Combinatorial properties of the oscillation map, L groups and higher dimensions

Place: Fields Institute (Room 210)

Dates: October 2nd, 2015 (13:30-15:00) and October 9th, 2015 (12-1:20)

Speaker: Yinhe Peng

Title: Combinatorial properties of the oscillation map, L groups and higher dimensions

Abstract: This is a joint work with Liuzhen. We investigated the oscillation map introduced by Justin Moore and found more combinatorial properties. It turns out that these properties can be used to construct an L group with non-Lindelof square. These can also reduce the dimension of certain spaces. We will construct, for each natural number n, an L space whose n-th power is an L space while n+1-th power is not. At last, we will discuss higher dimensional properties of the oscillation map itself.

## Alan Dow: An application of ZFC to Topology

Place: Fields Institute (Room 210)

Date: September 25th, 2015 (13:30-15:00)

Speaker: Alan Dow

Title: An application of ZFC to Topology

Abstract: A space  X  is said to be  M-dominated  for a metric space  M  if there is a covering of  X by compact sets that is order-preservingly indexed by the compact subsets of  M.  Of special interest is when  M  is the irrationals,  we may denote as P. This gave rise to a question by  Cascales, Orihuela, and Tkachuk  as to whether a compact space with a  P-diagonal   (defined as  $X^2$ minus the diagonal is  P dominated)  is metrizable. Following up on their results  that a  YES answer holds if  X  has countable tightness, and further a YES answer follows from assuming that  the bounding number is greater than $\omega_1$, we earlier proved with David Guerrero Sanchez, that CH also implies a YES answer. We report on a new result, with K.P. Hart,  that the answer is YES in ZFC.

## Peter Nyikos: Monotone normality, generalizations and independence results

Place: Fields Institute (Room 210)

Date: September 18th , 2015 (15:30-17:00)

Speaker: Peter Nyikos

Title: Monotone normality, generalizations and independence results

Abstract: Monotonically normal spaces have some very strong properties, despite their
modest-seeming definition. This talk has to do with some of these properties, and with set-theoretic consistency and independence  results having to do with them. Some of these independence results have to do with monotonically normal spaces themselves. Others are about some classes of more general spaces that have some of the same strong properties, sometimes with additional assumptions. Here is a trio of pairs of theorems illustrating this last theme.

Theorem 1A: Every monotonically normal manifold of dimension >1 is metrizable.
Theorem 1B: If PFA(S)[S], then every hereditarily normal manifold of dimension >1 is metrizable.

Theorem 2A: Every locally compact monotonically normal space is either paracompact or has a closed copy of a regular uncountable cardinal.
Theorem 2B: If PFA + Axiom R, then every locally compact, hereditarily strongly collectionwise Hausdorff space is either paracompact or has a copy of $\omega_1$.

Theorem 3A: Every monotonically normal space has a normal product with [0,1].
Theorem 3B: If PFA(S)[S], then every hereditarily normal, locally compact space of countable extent has a normal product with [0,1].

Every monotonically normal space is hereditarily collectionwise normal, so each B theorem features a significant weakening of monotone normality.