Gabe Conant : Countable Homogeneous Metric Spaces Over Finite Spectra

Posted by Phillip Wesolek , part of the Graduate Student Colloquium.

At

April 10, 2014, 4:15 p.m.

In

SEO 636

Abstract

We introduce the Fraisse construction, which is a method for building countable homogeneous structures from certain classes of finite structures (called Fraisse classes). The focus of the talk will be on classes of finite metric spaces with distances from a particular finite set, which is fixed for the class. We present a characterization, called the four-values condition, of when theses classes are Fraisse classes, followed by examples and reformulations of this characterization. We then consider the first-order theory of the countable homogeneous Fraisse limit. Of special interest in this context is the strong order property, which is a combinatorial measurement of the complexity of a first order theory.