Borel Reducibility of Equivalence Relations, Lausanne, May 29, 2017

SGSLPS 2017 Spring meeting on “Borel Reducibility of Equivalence Relations”

Université de Lausanne (Unil), Amphipôle, Room 340

29 May 2017, 10:30 – 17:00

The SGSLPS 2017 Spring meeting on “Borel Reducibility of Equivalence Relations” will feature four hour-long talks by leading experts in the field. The first talk will be introductory and will aim at a general audience.

Speakers:

•  Andrew Brooke-Taylor (University of Leeds, Leeds)
• Raphaël Carroy (Kurt Gödel Research Centre, Vienna)
• Julien Melleray (Université Claude Bernard Lyon 1, Lyon)
• Luca Motto Ros (Università di Torino, Turin
Classification has always been a central theme in mathematics. The study of Borel Reducibility of Equivalence Relations deals with the classification of points of standard Borel spaces up to equivalence relations by explicit, or Borel, mappings between such spaces.

This idea gives rise to a notion of complexity of equivalence relations, and tools from Descriptive Set Theory are used to compare such relations and measure their complexities.

Organisers:
The SGSLPS 2017 Spring meeting is organised by the Swiss Graduate Society for Logic and Philosophy of Science, SGSLPS, with funding by the Swiss Academy of Sciences.
The Swiss Graduate Society for Logic and Philosophy of Science (SGSLPS) is an association of advanced undergraduate and graduate students with a distinctive interest in the large domains of logic and philosophy of science

James Cummings: Definable subsets of singular cardinals

Mathematical logic seminar – Apr 11 2017
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         James Cummings
Department of Mathematical Sciences
CMU

Title:     Definable subsets of singular cardinals

Abstract:

Shelah proved the surprising result that if μ is a singular strong limit cardinal of uncountable cofinality, then there is a subset X of μ such that all subsets of μ are ordinal-definable from X. We will give a proof and discuss some complementary consistency results.

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

Tuesday, April 18, 2017, from 4 to 5:30pm
East Hall, room 3096

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

Title: mathfrak p=mathfrak t, III

Abstract:

This is the third and last talk in the series (reasonably self-contained for those who missed any number of previous parts). 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.

Andrés Caicedo: Ramsey theory and small countable ordinals

Albion College, Mathematics Colloquium
April 13, 2017, 3:30 PM
Location:    Palenske 227

Speaker:    Andrés Eduardo Caicedo
(Associate Editor, Mathematical Reviews, Ann Arbor, MI)

Title:    Ramsey theory and small countable ordinals

Abstract:    I present a brief overview of classical Ramsey theory, and discuss some extensions in the context of small infinite ordinals.

http://mathcs.albion.edu/Colloquium_List.php?year=2016

Aleksander Cieślak: Indestructible tower

Tuesday, April 11, 2017, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Aleksander Cieślak (Wroclaw University of Science and Technology)

Title: Indestructible tower

Abstract:

Following the Kunen’s construction of m.a.d. family which is indestructible over adding $\omega_2$ Cohen reals we provide analogous construction for indestructibe tower.

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.