Logic Seminar
Chris Laskowski
University of Maryland
A simpler axiomatization of the Spencer-Shelah almost sure theories
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.
Monday April 10, 2006 at 4:00 PM in SEO 427