- 11am: Meet on the first floor of SEO if you're already here. We will leave to lunch at 11:20.
- 11:30am: Lunch at Joy Yee's
- 1pm:
**One talk** - 2:30:
**Two talk** - 4pm:
**Three talk** - 5:30pm: Dinner at Jaks Tap

It is probably easiest to park in the university parking lot on Morgan St. between Roosevelt and Taylor.

Steffen Lempp

Title: Spectra of computable models of disintegrated strongly minimal theories

Abstract: The investigation of which countable models of a given first-order theory are

The first strong negative result on spectra is due to Andrews and
A. Medvedev (2014) that for a strongly minimal disintegrated theory
*T* in a finite language, the only possible spectra are ∅, {0} and
[0, ω], in which case one can effectively (but non-uniformly) reduce to
the case of a binary relational language.

In this talk, will present on-going joint work with Andrews vastly extending this result. In particular, we are able to show:

- There are exactly seven possible spectra for strongly minimal disintegrated theories in a (possibly infinite) binary relational language.
- There are exactly ten possible spectra for strongly minimal disintegrated theories in a relational language of bounded arity in which each relation has Morley rank at most 1.
- The only additional possible spectra for strongly minimal disintegrated theories in a relational language of unbounded arity in which each relation has Morley rank at most 1 are of the form [0, α) or [0, α) ∪ {ω}.
- There are at most eighteen possible spectra for strongly minimal disintegrated theories in a ternary relational language.

Gabriel Conant

Title: Stable groups and expansions of the integers

Abstract: Motivated by a question of Marker on stable expansions of the group of integers, we give a characterization of superstable groups of finite U-rank, which uses model theoretic weight together with chain conditions on definable subgroups. Combined with recent work of Palacin and Sklinos, we conclude that the group of integers has no proper stable expansions of finite weight, and thus none of finite dp-rank. We finish with a brief discussion of other results on expansions of the integers, including open questions about the unstable, finite dp-rank case. This is joint work with Anand Pillay.

H. Jerome Keisler

Title:Randomizations of Scattered Sentences

Abstract: In 1970, Morley introduced the notion of an infinitary sentence being scattered. He showed the number of (isomorphism types of) countable models is at most aleph one for a scattered sentence, and is continuum for a non-scattered sentence. The absolute form of Vaught's conjecture says that a scattered sentence has at most countably many countable models. Generalizing previous work of Ben Yaacov and the author, we introduce here the notion of a separable randomization of an infinitary sentence, which is a separable continuous structure whose elements are random elements of countable models of the sentence. We improve a result by Andrews and the author, showing that an infinitary sentence with countably many countable models has few separable randomizations, that is, every separable randomization is isomorphic to a very simple structure called a basic randomization. We also show that an infinitary sentence with few separable randomizations is scattered. Hence if the absolute Vaught conjecture holds, then a sentence has few separable randomizations if and only if it has at most countably many countable models, and also if and only if it is scattered. Moreover, assuming Martin's axiom for aleph one, we show that every scattered sentence has few separable randomizations.

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