John Baldwin : A field guide to Hrushovski constructions

Posted by , part of the Logic Seminar.

At

May 18, 2009, 10:30 a.m.

In

SEO 612

Abstract

Hrushovski generalized the Fraisse construction to provide counter examples to two major conjectures in model theory. Baldwin and Shelah adapted one of these arguments to give the first full proof of the Spencer-Shelah 0-1 laws for random graphs with edge probability \$n^{-\alpha}\$. Recently, Baudisch, Hils, Martin-Pizzaro and Wagner used the method to construct expansions of algebraically closed fields with a definable subgroup of the multiplicative group. We will try to give an organized account of the 40 or 50 constructions using this method and suggest some further open problems. In particular, we will describe the essential ideas of Laskowski's significantly simplification of the random graph argument.

seminar begins with tea.