Yang Yue: On a Question of Cholak and Downey

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 17 September 2014, 17:00 hrs

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

Speaker: Yang Yue

Title: On a Question of Cholak and Downey

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

In a paper entitled “On the Cantor-Bendixon rank of recursively
enumerable sets” (JSL 1993), Cholak and Downey showed that for every
recursive ordinal alpha and every nonrecursive r.e. degree d,
there is an r.e. set of rank alpha and degree d.
They also asked if one can generalize the result to
Delta-0-2 degrees, i.e., for every recursive
ordinal alpha and every nonrecursive Delta-0-2
degree d there is a Delta-0-2 set of rank
alpha and degree d. I will show the answer is positive.

This is a joint work with Rod Downey and Guohua Wu.

Clinton Conley: An introduction to Borel graph theory

Mathematical logic seminar – September 16, 2014
Time:     12:30 – 13:50Room:     Wean Hall 8220

Speaker:         Clinton Conley
Department of Mathematical Sciences
Carnegie Mellon University

Title:     An introduction to Borel graph theory

Abstract:

We discuss the theory of Borel graphs on standard Borel spaces, which has been a fertile topic of research in recent decades. While results in this purely Borel context are interesting on their own, we pay special attention to the “measure-theoretic” context in which the underlying space is equipped with a standard probability measure and null sets are discarded at one’s fancy. Results in this setting have connections with a variety of areas of mathematics including graph limits, ergodic theory, and probability. Our particular goals for this talk, after defining various notions, are to show ease of coloring graphs with $\mu$-a.e. hyperfinite connectedness relation and to construct examples of graphs which are hard to color.

Model Theory Seminars on Monday 5-6:30PM 9/15 & 9/22

 

Model Theory Seminar
 
Adam Gutter
 
Carnegie Mellon University

Title:   Superstable Fields and Groups – Part I

Abstract:  This series of talks will focus on proving a theorem of Cherlin and Shelah

(1980): If F is an infinite field with a superstable theory, then F is algebraically closed. This extends a result by Macintyre (1971) which states that any infinite omega-stable field is algebraically closed. The proof proceeds via results about stable groups, which are applied to the additive and multiplicative groups of a field F, along with the superstability assumption and elementary Galois theory.

The first talk will focus on an indecomposability theorem for stable groups (which we will later apply to our field).

 
Date: Monday, September 15, 2014
Time: 5:00 – 6:30 PM
Location: Wean 8220
—————————————————————————
Model Theory Seminar
 
Adam Gutter
 
Carnegie Mellon University

Title:   Superstable Fields and Groups – Part II

Abstract:  This series of talks will focus on proving a theorem of Cherlin and Shelah

(1980): If F is an infinite field with a superstable theory, then F is algebraically closed. This extends a result by Macintyre (1971) which states that any infinite omega-stable field is algebraically closed. The proof proceeds via results about stable groups, which are applied to the additive and multiplicative groups of a field F, along with the superstability assumption and elementary Galois theory.

The first talk will focus on an indecomposability theorem for stable groups (which we will later apply to our field).

Date: Monday, September 22, 2014

Time: 5:00 – 6:30 PM
Location: Wean 8220

Konstantinos Tyros: A disjoint union theorem for trees.

Friday 12 September Fields Institute, Room 210, 13:30-15:00

Speaker: Konstantinos Tyros.
Title:  A disjoint union theorem for trees.
Abstract: In this talk we will present an infinitary disjoint union theorem for level products of trees. An easy consequence of the dual Ramsey theorem due to T.J. Carlson and S.G. Simpson is that for every Suslin measurable finite coloring of the power set of the natural numbers, there exists a sequence $(X_n)_{n\in\mathbb{N}}$ of disjoint non-empty subsets of $\mathbb{N}$ such that the set
\[\Big\{\bigcup_{n\in Y}X_n:\; Y\;\text{non-empty subset of }\mathbb{N}\Big\}\]
is monochromatic. The result that we will present is of this sort, where the underline structure is the level product of a finite sequence of uniquely rooted and finitely branching trees with no maximal nodes of height $\omega$ instead of the natural numbers.
As it is required by the proof of the above result, we develop an analogue of the infinite dimensional version of the Hales–Jewett Theorem for maps defined on a level product of trees, which we will also present, if time permits.

Thomas Forster: WQOs and BQOs

Wednesday, September 10 from 3 to 4pm
Room: Math 226
Speaker: Thomas Forster (Cambridge)
Title: WQOs and BQOs – an Introductory Talk

Abstract: A WQO is a transitive reflexive relation with no infinite antichains and no infinite strictly descending chains. In this introductory talk (very few proofs!) for a general mathematical audience i shall try to show some of the many places that WQOs have spread their tentacles into, how they give rise to BQOs, the connections with finite combinatorics (Seymour-Robertson theorem), undecidability results in arithmetic and other fun stuff. I’ll even tell you what the two TLAs stand for.

Jacob Davis: Families of universal graphs at successors of singulars.

CMU Math Logic Seminar Tuesday 9 September 12:30.   Seminar will meet at 12:30 in Wean Hall 8220.

Speaker: Jacob Davis

Title: Families of universal graphs at successors of singulars.

Abstract:We will discuss the result that for lambda a singular cardinal it is possible
to have a jointly universal family of graphs on lambda^+ that has size
lambda^{+2} whilst 2^{lambda^+}=lambda^{+3}. Our construction starts with a
supercompact cardinal kappa and ends by performing either Prikry or Radin
forcing to convert kappa into the desired singular cardinal. However in between
we conduct a preparatory iteration to manipulate the Prikry / Radin names for
graphs on kappa^+ into a suitable form. In general proving results at
successors of singular cardinals is challenging due to the limited number of
forcing constructions available, so this approach is likely to have wider
applications.

Appalachian Set Theory workshop: Slawomir Solecki

November 22, 2014, at the University of Illinois at Chicago

Slawomir Solecki

Ultrafilter space methods in Infinite Ramsey Theory

Professor Solecki will present a part of Infinite Ramsey Theory by explaining the methods and results stemming from Ellis’ idempotent lemma. These methods rely heavily on ultrafilters and their spaces and are far reaching generalizations of the initial argument due to Galvin and Glazer. The lectures will include proofs of older and more recent results, including the Furstenberg-Katznelson and Gowers theorems. The lectures will present a a new unified treatment of this part of Infinite Ramsey Theory, including some applications if time allows.

Here is a reading list containing some background material for the workshop:

 

  • Basics:
    • The ultrafilter entry on Wikipedia.
    • Pages 409-413 in W. Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409-419.
  • Intermediate:
    • Sections 2 and 3 in V. Bergelson, A. Blass, N. Hindman, Partition theorems for spaces of variable  words, Proc. London Math. Soc. 68 (1994), 449-476.
  • Advanced:
    • H. Furstenberg, Y. Katznelson, Idempotents in compact semigroups and Ramsey theory,   Israel J. Math. 68 (1989), 257-270.
    • Chapter 2 in S. Todorčević, Introduction to Ramsey Spaces, Annals of Mathematics Studies, 174. Princeton University Press, 2010.

 

  • Supplementary:
    • Chapters 1-5 in  N. Hindman, D. Strauss, Algebra in the Stone-Čech Compactification, de Gruyter  Expositions in Mathematics 27, Walter de Gruyter & Co., 2012.

Diana Ojeda: Finite forms of Gowers’ Theorem on the oscillation stability of $c_0$

5 September 2014, 13:30–15:00

Fields institute, Room 210

Speaker: Diana Ojeda

Title:  Finite forms of Gowers’ Theorem on the oscillation stability of $c_0$
Abstract: We give a constructive proof of the finite version of Gowers’ $FIN_k$ Theorem and analyze the corresponding upper bounds. The $FIN_k$ Theorem is closely related to the oscillation stability of $c_0$. The stabilization of Lipschitz functions on arbitrary finite dimensional Banach spaces was proved well before by V. Milman. We compare the finite $FIN_k$ Theorem with the Finite Stabilization Principle found by Milman in the case of spaces of the form $\ell_{\infty}^n$, $n\in N$, and establish a much slower growing upper bound for the finite stabilization principle in this particular case.

Münster conference on fine structure and inner model theory, July 20-24, 2015

Münster conference

on fine structure and inner model theory

Institut für Mathematische Logik, WWU Münster,

July 20 — 24, 2015

Organizers: Ralf Schindler (Münster), John Steel (Berkeley)

People who expressed their intention to participate: Dominik Adolf (Berkeley), Sean Cox (VCU), Qi Feng (Beijing), Gabriel Fernandes (Münster), Gunter Fuchs (CUNY), Ronald Jensen (Berlin), Menachem Magidor (Jerusalem), Grigor Sargsyan (Rutgers), Ralf Schindler (Münster), Farmer Schlutzenberg, John Steel (Berkeley), Nam Trang (CMU), Sandra Uhlenbrock (Münster), Trevor Wilson (Irvine), W. Hugh Woodin (Harvard), Yizheng Zhu (Münster), Martin Zeman (Irvine).

Meeting in honor of Hugh Woodin’s 60th birthday, April 17-19, 2015

Conference in Honor of Hugh Woodin’s 60th Birthday

The meeting in honor of Hugh Woodin’s 60th birthday will be held on April 17-19, 2015, at Harvard University.

Conference Speakers

Additional information will be posted there as it becomes available.
The organizers ask those planning to attend to write to woodinbirthdayconference@gmail.com to indicate their intent.