## Dilip Raghavan: Real games and strategically selective coideals, Part 2.

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 7 October 2015, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Dilip Raghavan

Title: Real games and strategically selective coideals, Part 2.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

A classical theorem of Mathias says that the Axiom of Determinacy for
Real games (AD_R) implies that there are no tall selective coideals on
omega. Farah introduced the notion of a semiselective coideal and
proved in ZF that these are precisely those ideals on omega whose
quotient adds a selective ultrafilter. It is unkown whether AD_R
implies the non-existence of tall semiselective coideals. We introduce
the notion of strategically selective coideal, and show that tall
strategically selective coideals do not exist under AD_R. The Axiom of
Choice implies that the notions of semiselective and strategically
selective coideal coincide.
This talk is a continuation of the talk from 16/09/2015 and will
provide more mathematical details and selected proofs.
This is joint work with Paul Larson.

## Miguel Angel Mota Gaytán: Baumgartner’s Conjecture and Bounded Forcing Axioms (Part I)

Abstract: Using some variants of weak club guessing we separate some fragments of the proper forcing axiom: we show that for every two indecomposable ordinals $\alpha < \beta$, the forcing axiom for the class of all the $\beta$-proper posets does not imply the bounded forcing axiom for the class of all the $\alpha$-proper posets.

Set theory seminar, Mexico City, Wednesday October 7, 2015 at  IMATE, UNAM, Salón Graciela Salicrup 16:00.

## Andrés Caicedo: The Haddad-Sabbagh results in the partition calculus of small countable ordinals

Wednesday, October 7, 16:00 to 17:30 in 3096 East Hall

We present a survey of results announced 45 years ago by Haddad and Sabbagh on the partition calculus of ordinals. Part of the interest in these results is that they are obtained by reducing genuine infinitary combinatorics problems to purely finite (albeit unfeasible) ones.

## 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.

## Winter School, Jan 30 – Feb 6, 2016

We are pleased to announce that the registration for the Winter School in Abstract Analysis, section Set Theory & Topology is now open. The conference will take place between Jan 30th and Feb 6th 2016 in Hejnice, Czech Republic.

Tutorial speakers for this year are:

Martin Goldstern
Thomas Jech
Yiannis N. Moschovakis
Lyubomyr Zdomskyy

The conference fee is 300 EUR and covers all expenses including the bus from Prague to Hejnice and back. Accommodation will be in double rooms.

We have a limited amount of money to support participation of young researchers, students, and participants with limited funding options.

Dec 9th, 2014 fee waiver application deadline
Dec 31st, 2014 registration deadline

www.winterschool.eu

If you have any questions please do not hesitate to contact us.

We hope to see you in January,

David Chodounsky, Jan Stary and Jonathan Verner

## Clinton Conley: Borel marker sets and hyperfiniteness

[this talk is a warmup for the Appalachian set theory workshop at CMU on October 24,
where Su Gao (UNT) will speak on “Countable abelian group actions”]

Mathematical logic seminar – September 29, 2015
Time:     12:30 – 13:30

Room:     Wean Hall 7201

Speaker:         Clinton Conley
Department of Mathematical Sciences
CMU

Title:     Borel marker sets and hyperfiniteness

Abstract:     A classical tool in ergodic theory is the Rokhlin lemma, which more or less states that any ergodic measure-preserving automorphism of a standard probability space is the uniform limit of periodic automorphisms. At its combinatorial core, the lemma’s proof relies on the ability to find measurable sets which intersect every orbit in a reasonably spaced out fashion. We discuss analogs of this in the purely Borel context, and use such marker sets to prove the Slaman-Steel / Sullivan-Weiss-Wright result that every Borel action of the integers on a standard Borel space generates a hyperfinite orbit equivalence relation. Time permitting, we discuss the (still open) problem of extending this to actions of arbitrary countable amenable groups, in preparation for Su Gao’s Appalachian Set Theory workshop this October.

## Liljana Babinkostova: The selective strong screenability game

Wednesday, September 30 from 3 to 4pm
Room: MP 207
Speaker: Liljana Babinkostova (BSU)
Title: The selective strong screenability game

Abstract: Selective versions of screenability and of strong screenability coincide in a large class of spaces. We show that the corresponding games are not equivalent in even such standard metric spaces as the closed unit interval. We identify sufficient conditions for ONE to have a winning strategy, and necessary conditions for TWO to have a winning strategy in the selective strong screenability game.

## Chong Chi Tat: Ramsey’s Theorem on Trees

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 30 September 2015, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Chong Chi Tat

Title: Ramsey’s Theorem on Trees.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Ramsey’s theorem on trees concerns the existence of a
monochromatic tree isomorphic to the full binary tree, for a given finite
colouring of the latter. The existence of a monochromatic perfect tree is
immediate in the system of Peano arithmetic. The interesting question is
to identify the weakest system that is sufficient for it. We will give a
progress report of our study.

This is joint work with Li Wei and Wang Wei.

## 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.