Chris Laskowski : A simpler axiomatization of the Spencer-Shelah almost sure theories

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

April 10, 2006, 4 p.m.

In

SEO 427

Abstract

Shelah and Spencer proved that when alpha is irrational in (0,1) there is an almost sure theory T of random graphs of size n, when the edge probability is n^{-alpha}. Somewhat later, Baldwin observed that the same theory T can be visualized as the theory of a generic object of a generalized Fraisse construction. We give an AE axiomatization of T and examine other countable models of T. Somewhat surprisingly, even though it can be uniquely characterized as being a Fraisse limit, the generic does not appear to be any particularly `special' model of T. We will also discuss applicability of these methods to other Fraisse constructions.