Logic Archives for Academic Year 2013


Organizational Meeting

When: Tue, September 4, 2012 - 3:30pm
Where: Math 1311


Salvaging Kikyo-Shelah

When: Tue, September 11, 2012 - 3:30pm
Where: Math 1311
Speaker: Koushik Pal (UMD) - http://www2.math.umd.edu/~koushik/
Abstract: Kikyo and Shelah showed that if T is a first-order theory in some language L with the strict-order property, then the theory T_\sigma, which is the old theory T together with an L-automorphism \sigma, does not have a model companion in L_\sigma, which is the old language L together with a new unary predicate symbol \sigma. However, it turns out that if we add more restrictions on the automorphism, then T_\sigma can have a model companion in L_\sigma. I will show some examples of this phenomenon in two different context - the linear orders and the ordered abelian groups. In the context of the linear orders, we even have a complete characterization of all model complete theories extending T_\sigma in L_\sigma. This is a joint work with Chris.

Countable models of omega-stable theories

When: Tue, September 25, 2012 - 3:30pm
Where: MTH 1311
Speaker: Chris Laskowski (UMD) - http://www2.math.umd.edu/~laskow/

Polyadic groups

When: Tue, October 2, 2012 - 3:30pm
Where: MTH 1311
Speaker: Alexei Kolesnikov (Towson University) - http://pages.towson.edu/akolesni/
Abstract: A polyadic group (or n-group) is a set with an n-ary operation that satisfies certain natural properties. In this talk, I will introduce the polyadic groups and related objects and will survey some of the results that describe the nature of such groups.

Polyadic groups Part II

When: Tue, October 9, 2012 - 3:30pm
Where: MTH 1311
Speaker: Alexei Kolesnikov (Towson University) - http://pages.towson.edu/akolesni/
Abstract: A polyadic group (or n-group) is a set with an n-ary operation that satisfies certain natural properties. In this second talk, I will describe the results related to Hosszu -- Gluskin theorem about the n-ary groups.

Properties of automorphisms of saturated models of PA

When: Tue, October 16, 2012 - 3:30pm
Where: MTH 1311
Speaker: Ermek Nurkhaidarov (Penn State - Mont Alto) - http://www.ma.psu.edu/Academics/31215.htm

A Model-Completeness Result for the Real Exponential Field

When: Tue, October 23, 2012 - 3:30pm
Where: MTH 1310
Speaker: Richard R. Rast (UMD) - http://terpconnect.umd.edu/~rastr/

Valued Difference Fields and NTP_2

When: Tue, November 6, 2012 - 3:30pm
Where: MTH 1311
Speaker: Koushik Pal (UMD) - www2.math.umd.edu/~koushik

When Prime Models are not Unique

When: Tue, November 13, 2012 - 3:30pm
Where: MATH 1311
Speaker: Dr. Chris Laskowski (UMCP) -

Introduction to PCF-Theory

When: Tue, November 20, 2012 - 3:30pm
Where: MATH 1311
Speaker: Tim Mercure (UMCP) -

Introduction to PCF-Theory Part II

When: Tue, November 27, 2012 - 3:30pm
Where: MTH 1311
Speaker: Tim Mercure (UMD) -

An Introduction to Hrushovski Constructions

When: Tue, December 4, 2012 - 3:30pm
Where: MTH 1311
Speaker: Justin Brody (Goucher College) -

Generic structures and NSOP_4

When: Tue, December 11, 2012 - 3:30pm
Where: MTH 1311
Speaker: Koichiro Ikeda (Hosei University, Japan) -
Abstract: Evans-Wong proved if a generic structure is omega-categorical then the theory has NSOP_4.
In this talk, we generalize this result.

Slides: https://docs.google.com/open?id=0B-ow7NaULJE0dTNSUXA3TThGQWc

Organizational Meeting

When: Tue, January 29, 2013 - 3:30pm
Where: MTH 1311
Speaker: () -

From combinatorial complexity to triangulations of monotone families

When: Tue, February 5, 2013 - 3:30pm
Where: MTH 1311
Speaker: Saugata Basu (Purdue University) - http://www.math.purdue.edu/~sbasu/
Abstract: I will explain how to extend the combinatorial parts of certain well known bounds on the topology (the Betti numbers) of semi-algebraic sets to the general o-minimal setting and mention some applications of such bounds in discrete geometry.
In the second part of the talk I will explain a result of Gabrielov and Vorobjov which reduces the problem of bounding the topology of arbitrary definable sets to that of compact ones, and show how it leads to the problem of proving the existence of triangulations compatible with monotone definable families. I will mention some partial results in this direction.

(The last part of the talk is joint work with A. Gabrielov and N. Vorobjov.)

Fields with operators

When: Tue, February 12, 2013 - 3:30pm
Where: MTH 1311
Speaker: Koushik Pal (UMD) - www2.math.umd.edu/~koushik

Polygroupoids and type-amalgamation properties

When: Tue, February 26, 2013 - 3:30pm
Where: MTH 1311
Speaker: Alexei Kolesnikov (Towson University) -
Abstract: In [1], Hrushovski linked the failure of 3-uniqueness to the existence of a definable groupoid witnessing such failure. He remarked that a continuation of the result to the failure of n-uniqueness, for n greater than 3, would be of interest. This talk is an exposition of my joint work with Goodrick and Kim, in which we define the objects that witness the failure of n-uniqueness, develop their model-theoretic properties, and show that any failure of n-uniqueness must be witnessed by one of these objects.

A red herring. Approaches toward settling Vaught's Conjecture.

When: Tue, March 5, 2013 - 3:30pm
Where: MTH 1311
Speaker: Chris Laskowski (UMD) -

Polygroupoids and type-amalgamation properties, Part 2

When: Tue, March 12, 2013 - 3:30pm
Where: MTH 1311
Speaker: Alexei Kolesnikov (Towson University) -
Abstract: This talk continues an exposition of my joint work with Goodrick and Kim, in which we define the objects that witness the failure of n-uniqueness, develop their model-theoretic properties, and show that any failure of n-uniqueness must be witnessed by one of these objects. The second part will be devoted to the associativity properties and to a certain group action on the polygroupoids.

Simple Generic Structures

When: Tue, March 26, 2013 - 3:30pm
Where: MTH 1311
Speaker: Justin Brody (Goucher College) -
Abstract: In [1], Pourmahdian developed a framework for determining the simplicity of generic structures and produced an unstable example. I will present an overview of his paper. If time permits, I will discuss another example which I believe to be simple and make some comments on the obstructions to using Pourmahdian's framework to prove it.

1. Pourmahdian, Massoud. "Simple generic structures." Annals of Pure and Applied Logic 121.2 (2003): 227-260.

Automorphisms of models of arithmetic: recognizing some basic subgroups

When: Tue, April 9, 2013 - 3:30pm
Where: MTH 1311
Speaker: Ermek Nurkhaidarov (Penn State - Mont Alto) -
Abstract: In the talk we discuss the automorphism group of a countable recursively saturated model of Peano Arithmetic. We show that it recognizes gap stabilizers as well as stabilizers of elements realizing minimal type.

Indiscernibles for the Constructible Universe

When: Tue, April 16, 2013 - 3:30pm
Where: MTH 1311
Speaker: Tim Mercure (UMD) -

Algebraic methods for multivariate splines.

When: Tue, April 23, 2013 - 3:30pm
Where: MTH 1311
Speaker: Alexei Kolesnikov and Tatyana Sorokina (Towson University) -
Abstract: This two-part talk will describe the main aspects of research in the area of multivariate splines and the algebraic geometry methods currently used in this field. The first part of the talk will focus on the classical methods used in studying multivariate splines; the second part will discuss the methods of algebraic geometry used to compute the dimension of certain spline spaces. The talk will conclude with the discussion of open questions.

Algebraic methods for multivariate splines, Part 2.

When: Tue, April 30, 2013 - 3:30pm
Where: MTH 1311
Speaker: Alexei Kolesnikov and Tatyana Sorokina (Towson University) -
Abstract: The second talk in the series of two will describe some of the algebraic geometry methods currently used to answer questions in the field of approximation theory. We will focus on the methods of algebraic geometry used to compute the dimension of certain spline spaces. We will show that the spline spaces can be viewed as a certain homology module and will describe the chain complex that is used to compute the dimension of the homology module. The talk will conclude with the discussion of open questions.

Few models in aleph_1 implies a form of exchange.

When: Tue, May 7, 2013 - 3:30pm
Where: MTH 1311
Speaker: John Baldwin (UIC) -
Abstract: We will expound the following theorem of Shelah:
If a sentence of L_{omega_1, omega} has fewer than 2^{aleph_1} models in aleph_1, then pseudo-closure satisfies exchange (locally). (This requires understanding the notion of pseudo-closure and then a forcing argument.)

This exposition is joint with Laskowski and depends heavily on discussions with Koerwien and Larson as well as Shelah.

A Proof of Vaught’s Conjecture for ℵ_0–Stable Theories

When: Wed, May 15, 2013 - 3:30pm
Where: MTH 1310
Speaker: Maxx Cho (UMD) -