Category Archives: Seminars

Francisco Guevarra Parra: An application of the the Ultra-Ellentuck theorem

Place: Fields Institute (Room 210)

Date: April 7, 2017 (14:15-15:00)

Speaker: Francisco Guevara Parra

Title: An application of the the Ultra-Ellentuck theorem

Abstract: We will use the Ultra-Ellentuck theorem to construct countable
local $\pi$-bases in a given sequential-definable topology on $\omega$
that is $p^+$ (or $\alpha_4$ if we replace sequential by Frechet).

Yuan Yuan Zheng: The Ehrenfeucht Game

Place: Fields Institute (Room 210)

Date: April 7, 2017 (13:30-14:15)

Speaker: Yuan Yuan Zheng, University of Toronto

Title: The Ehrenfeucht Game

Abstract: The Ehrenfeucht Game is interesting in its own right as a game.
It was originally a method given by Roland Fraïssé to verify elementarily
equivalence. It was reformulated as a game by Andrzej Ehrenfeucht. We will
define the game, see how it plays a role in deciding whether a property is
first order expressible, and give a vague idea of how it relates to the
Zero-One Law.

Thilo Weinert: Partitioning pairs of sigma-scattered linear orders

BIU seminar in Set Theory

On 20/04/2017, 10-12, Building 604, Room 103

Speaker:  Thilo Weinert

Title: Partitioning pairs of sigma-scattered linear orders

Abstract. We are going to continue the analysis of generalised scattered orders, proving the result described towards the end of Chris Lambie-Hanson’s talk. This states that consistently, for every sigma-scattered linear ordering there is a colouring of its pairs in black & white such that every triple contains a white pair and every copy of one of the following order-types contains a black pair:

  • omega_1^omega
  • (omega_1^omega)^*
  • omega_1 * (omega * omega^*)^omega
  • omega_1^* * (omega * omega^*)^omega
  • (omega * omega^*)^omega * omega_1
  • (omega * omega^*)^omega * omega_1^*

This generalises a 46-year-old Theorem of Erdős & Rado about ordinals. A sufficient hypothesis implying this theorem is the existence of a colouring of the pairs of omega_1 * omega in black & white such that every triple contains a black pair and every subset of full order-type contains a white one. Time permitting we may present a proof that stick = b = Aleph_1 implies the existence of such a colouring. Here b is the unbounding number and stick = Aleph_1 is a weakening of the club principle which was considered by Baumgartner 41 years ago, named by Broverman, Ginsburg, Kunen & Tall two years thereafter and twenty years ago reconsidered as a cardinal characteristic by Fuchino, Shelah & Soukup.

Assaf Rinot: Distributive Aronszajn trees

Forcing Seminar (Tel-Aviv University)

Tuesday, 4/Apr/2017, 9-11.
Room 007, Schriber building, Tel-Aviv University.

Speaker: Assaf Rinot

Title: Distributive Aronszajn trees

Abstract: We address a conjecture asserting that, assuming GCH, for every singular cardinal $\lambda$, if there exists a $\lambda^+$-Aronszajn tree, then there exists one which is moreover $\lambda$-distributive.

Peter Holy: Small embedding characterizations for large cardinals, and internal large cardinals

KGRC Research Seminar – 2017‑04‑06 at 4pm

Speaker: Peter Holy (University of Bonn, Germany)

Abstract:

Many notions of large cardinals are characterized in terms of the existence of certain elementary embeddings with the large cardinal in question as their critical point. A small embedding characterization of a large cardinal notion is one that requires the existence of certain elementary embeddings that map their critical point to the relevant large cardinal. One classic example of such a small embedding characterization is Magidor’s small embedding characterization of supercompactness. We show that many other large cardinal notions have small embedding characterizations, in particular also large cardinal notions for which no embedding characterizations have been known to exist at all.

In the second part of this talk, I will then sketch an application of small embedding characterizations, that yields what we call internal large cardinals, which essentially describe what is left of large cardinals after they have been destroyed or collapsed by sufficiently nice forcing. The basic idea is to lift the small embeddings that characterize the initial large cardinals.

This is joint work with Philipp Lücke.

Omer Mermelstein: Closed ordinal Ramsey numbers below $\omega^\omega$

BGU seminar in Logic, Set Theory and Topology
Time: Tuesday, April 4th, 12:15-13:30.
Place: Seminar room -101, Math building 58.
Speaker: Omer Mermelstein (BGU)

Title: Closed ordinal Ramsey numbers below $\omega^\omega$

Abstract:Since the 1950s, many versions of the partition calculus and arrow notation, introduced by Erdős and Rado, were studied. One such variant, introduced by Baumgartner and recently studied by Caicedo and Hilton, is the closed ordinal Ramsey number. For this variant, we require our homogeneous subset to be both order-isomorphic and homeomorphic to a given ordinal.

In the talk we present an approach with which to tackle this flavour of partition calculus, and if time permits prove some results. The talk is elementary and self-contained.

Marion Scheepers: Playing an infinitely long game when you have limited memory (IV)

Tuesday, April 4 from 3 to 4pm
Room: MB 124
Speaker: Marion Scheepers (BSU)
Title: Playing an infinitely long game when you have limited memory (IV)

Abstract: We consider a class of infinite games in which player TWO has a winning strategy (based on perfect memory). In prior talks in this series we considered the effect of a limited memory where TWO remembers only the most recent move of ONE and of TWO, or TWO remembers a limited number of prior moves of ONE only.

As in these prior talks we consider the game where ONE chooses a first category subset of a space, and TWO chooses a nowhere dense set each inning. ONE’s sets are strictly increasing from inning to inning. For a fixed k, TWO remembers only the most recent k moves of ONE. We discussed why for k=1 only in the simplest of circumstances TWO has a winning 1-tactic. We also outline how in certain examples TWO had a winning 2-tactic ($k=2$). In this talk we will focus on the case when TWO does not have a winning 2-tactic, but does have a winning k-tactic for some $k>2$.

David J. Fernández Bretón: mathfrak p=mathfrak t, II

Thursday, April 6, 2017, from 4 to 5:30pm
East Hall, room 3088

Speaker: David J. Fernández Bretón (University of Michigan)

Title: mathfrak p=mathfrak t, II

Abstract:

This is the second in a series of (hopefully at most) three talks, and it will be reasonably self-contained for those who missed the first part. I will continue to present the proof, due to Maryanthe Malliaris and Saharon Shelah in 2012, that the cardinal invariants p and t are equal, which constitutes an extremely important result in the theory of Cardinal Characteristics of the Continuum.

Juan Carlos Martínez: On the existence of pcf algebras

Speaker: Juan Carlos Martínez   (Universitat de Barcelona)

Title: On the existence of pcf algebras

Abstract: We shall give a direct proof of a result of Jech
and Shelah on the existence of a type of pcf algebras on
ω1.

Date: Thursday, 6 April 2017

Time: 15:30

Place: Room T-2*
Department of Mathematics & Computer Science
University of Barcelona
Gran Via de les Corts Catalanes 585
08007 Barcelona

Timothy Trujillo: Parametrizing by the Ellentuck space

Place: Fields Institute (Room 210)

Date: March 31, 2017 (13:30-15:00)

Speaker: Timothy Trujillo, Colorado School of Mines

Title: Parametrizing by the Ellentuck space

Abstract: We introduce a new construct that can be used to parametrize some
topological Ramsey spaces by the collection of infinite subsets of the natural
numbers. We show that these parametrized spaces are also topological Ramsey spaces.Then we use these spaces to give new proofs of some known parametrized perfect set theorems. We conclude with a discussion of how to extend the results to the abstract setting and open questions related to applying the results to the Tukey theory of ultrafilters.