### Logic Archives for Academic Year 2013

#### Organizational Meeting

When: Tue, September 3, 2013 - 3:30pm
Where: Math 1311
Speaker: Organizational Meeting () -

#### On omega1-categorical theories of abelian groups and fields

When: Tue, September 10, 2013 - 3:30pm
Where: Math 1311
Speaker: Koushik Pal (UMCP) -

#### Comparing prime and atomic models in uncountable languages

When: Tue, September 17, 2013 - 3:30pm
Where: Math 1311
Speaker: Chris Laskowski (UMCP) - math.umd.edu/~mcl
Abstract: For complete theories in uncountable languages, we show that very few implications exist between existence and uniqueness hypotheses for atomic, prime, and constructable models.

#### On maximal subgroups in the automorphism group of a model of arithmetic

When: Tue, September 24, 2013 - 3:30pm
Where: Math 1311
Speaker: Ermek Nurkhaidarov (Penn State, Mont Alto) -

#### Some Uses for Generic Models

When: Tue, October 1, 2013 - 3:30pm
Where: Math 1311
Speaker: Tim Mercure (UMCP) -

#### On dense independent subsets of geometric structures

When: Tue, October 8, 2013 - 3:30pm
Where: Math 1311
Speaker: Yevgeniy Vasilyev (Memorial University of Newfoundland and Christopher Newport University) -
Abstract: We consider an expansion of a geometric theory obtained by adding a predicate distinguishing a "dense" independent subset, generalizing a construction introduced by A. Dolich, C. Miller and C. Steinhorn in the o-minimal context. We show that the expansion preserves many of the properties related to stability, simplicity, rosiness and NIP. We also study the structure induced on the predicate, and show that while having a trivial geometry, it inherits most of the "combinatorial" complexity of the original theory.
This is a joint work with A. Berenstein.

#### Borel completeness of some o-minimal theories

When: Tue, October 15, 2013 - 3:30pm
Where: Math 1311
Speaker: Richard Rast (UMCP) -

#### Building models of size continuum in omega steps

When: Tue, October 29, 2013 - 3:30pm
Where: Math 1311

#### NO SEMINAR THIS WEEK

When: Tue, November 12, 2013 - 3:30pm
Where: MATH 1311
Speaker: () -

#### On VC-Minimal Theories

When: Tue, November 19, 2013 - 3:30pm
Where: Math 1311
Speaker: Vincent Guingona (Notre Dame) -
Abstract: VC-minimality is a model theoretic property that generalizes both o-minimality and strong minimality. Many interesting theories are VC-minimal, including algebraically closed valued fields. In my talk, I discuss recent developments in the study of VC-minimal theories. First, I examine the problem of computing VC-density in VC-minimal theories. Then, I consider the problem of classifying VC-minimality. For this, I define a new notion called dp-smallness and use this to help distinguish between VC-minimal and non-VC-minimal theories. I conclude with a proof that all VC-minimal ordered fields are real closed.

#### Computable Stability Theory

When: Wed, December 11, 2013 - 2:00pm
Where: Math 3206
Speaker: Uri Andrews (University of Wisconsin) -
Abstract: Stability theory attempts to classify the underlying structure of
mathematical objects. The goal of computable mathematics is to understand
when mathematical objects or constructions can be demonstrated computably.
I'll talk about the relationship between underlying structure and
computation of mathematical objects.

#### When is aleph_1 categoricity absolute?

When: Tue, February 4, 2014 - 3:30pm
Where: Math 1311

#### Must a unique atomic model be prime?

When: Tue, February 18, 2014 - 3:30pm
Where: Math 1311
Speaker: Douglas Ulrich (UMCP) -

#### Nonforking in Short and Tame Abstract Elementary Classes

When: Tue, February 25, 2014 - 3:30pm
Where: Math 1311
Speaker: Will Boney (Carnegie Mellon) -

#### Uniformly distinguishing aleph(n+1) from aleph(n)

When: Tue, March 11, 2014 - 3:30pm
Where: Math 1311
Abstract: We construct a uniform family of complete sentences phi(n) in L(omega1, omega) such that
each phi(n) has a model of size aleph(n) but no larger. These sentences have unusual amalgamation spectra.

#### Axiomatizing Abstract Elementary Classes

When: Tue, March 25, 2014 - 3:30pm
Where: Math 1311
Speaker: David Kueker (UMCP) -

#### Weakly one-based geometric theories

When: Tue, April 1, 2014 - 3:30pm
Where: Math 1311
Speaker: Yevgeniy Vasilyev (Memorial University of Newfoundland and Christopher Newport University) -
Abstract: In a joint work with Alexander Berenstein, we introduce several equivalent conditions, including weak local modularity, weak one-basedness and generic linearity, which provide a common generalization of the "classical" linearity notions used in the strongly minimal, supersimple SU-rank 1 and o-minimal settings, to the general class of geometric theories. One of our main tools, the lovely pair expansion, allows us to find a connection between linearity and the presence of vector spaces over division rings.

#### Characterizing Borel complete o-minimal theories

When: Tue, April 8, 2014 - 3:30pm
Where: Math 1311
Speaker: Richard Rast (UMCP) -

#### Maximal Automorphisms

When: Tue, April 15, 2014 - 3:30pm
Where: Math 1311
Speaker: Alf Dolich (CUNY -- Kingsborough Community College) -
Abstract: Given a model M, a maximal automorphism is one which fixes as few points in M as possible. We begin by outlining what the correct definition of "as few points as possible" should be and then proceed to study the notion. An interesting question arises when one considers the existence of maximal automorphisms of countable recursively saturated models. In particular an interesting dichotomy arises when one asks whether for a given theory T all countable recursively saturated models of T have a maximal automorphism. Our primary goal is to determine which classes of theories T lie on the positive side of this dichotomy. We give several examples of such classes. Attacking this problem requires a detailed understanding of recursive saturation, which we will also review in this talk.

#### Injective Structures which are not Locally Finite

When: Tue, April 22, 2014 - 3:30pm
Where: Math 1311
Speaker: Justin Brody (Goucher College) -
Abstract: Let $K$ be a class of structures and $\leq$ a notion of strong substructure on $K$.
We will discuss conditions under which the $(\K, \leq)$ admits a structure which is
injective (for $A \leq B$, strong embeddings of $A$ extend to strong embeddings of $B$) but not locally finite (there is some finite substructure which has no finite closure). We will also examine a conjecture of Larry Moss', which states that there is a such a structure for $K$ the class of finite graphs and $A \leq B$ whenever $A$ is isometric in $B$.

#### The small index property and models of Peano arithmetic

When: Tue, April 29, 2014 - 3:30pm
Where: Math 1311
Speaker: Ermek Nurkhaidarov (Penn State -- Mont Alto) -