MidWest Model Theory Day

Tuesday, October 23rd, 2012 at UIC


Speakers: Lynn Scow, Isaac Goldbring, Maryanthe Malliaris

Schedule: All talks are about an hour long, in SEO 636. There will also be coffee&cookies in 636.
It is probably easiest to park in the university parking lot on Morgan St. between Roosevelt and Taylor.
Let us know (@math.wisc.edu">andrewsmath.wisc.edu) if you are planning to come to lunch and/or dinner so we can make approximately correct reservations!

Titles & Abstracts:

Speaker: Lynn Scow
Title: Indiscernibles, EM-types, trees

Abstract: A generalized indiscernible is a set of parameters {a_i}_{i\subset I} in a model M indexed by an external structure I so that finite tuples from A have the same type in M, , provided the tuples of their indices have the same quantifier-free type in I. Generalized indiscernibles were introduced by Shelah in the 70's and have found a wide array of applications in classification theory. The EM-type of a generalized indiscernible is a means to encode the necessary first-order information in the indiscernible, and it can be a useful way to streamline compactness arguments. In this talk we will survey the uses of EM-types in working with generalized indiscernibles. As a consequence, we present a new Ramsey class of trees.

Speaker: Isaac Goldbring
Title: The fundamental group of a locally finite graph with ends: a hyperfinite approach

Abstract: It is well-known that the fundamental group of a finite, connected graph is a finitely generated free group, where one can take the chords of a spanning tree as a set of free generators. Diestel and Sprussel tried to give a similar combinatorial characterization of the end compactification of an infinite, locally finite, connected graph. They showed that the fundamental group embeds into a group of reduced words, where the words can have arbitrary countable order type and the notion of reduction is non-wellordered. Furthermore, they show that this group of reduced words embeds into an inverse limit of finitely generated free groups. In this talk, I will present a much simpler approach to this problem by showing how the fundamental group of the end compactification of a locally finite, connected graph embeds into the internal fundamental group of a hyperfinite (in the sense of nonstandard analysis) graph, which is then a hyperfinitely generated free group. I will discuss some applications of this result, including a simple proof that certain loops in the end compactification are non-nullhomologous. This is joint work with Alessandro Sisto.

Speaker: Maryanthe Malliaris
Title: Saturation of ultrapowers and the structure of unstable theories

Abstract: The talk will be about some very recent progress on Keisler's order, a far-reaching program of understanding basic model-theoretic structure through the lens of regular ultrapowers. I will explain Keisler's order and the perspective it gives on classifying the unstable theories, and discuss a recent paper of Malliaris and Shelah which applies model-theoretic techniques developed for the study of Keisler's order to solve a problem on cardinal invariants of the continuum.

Organizers:
Uri Andrews
Lynn Scow

Other MWMTDs:
April 5th, 2016
October 28th, 2014
October 22nd, 2013
April 18th, 2013
October 23rd, 2012
April 26th, 2012
October 11th, 2011
April 7th, 2011
October 26th, 2010