Kurt Gödel Research Center

2009 seminar talk: A universality spectrum for graphs without GCH

Talk held by Katie Thompson (KGRC) at the KGRC seminar on 2009-01-29.

Abstract

A universal model for structures of size K is one which embeds all other such structures of size K. For first-order theories of small size, like graphs, there are universals in all infinite cardinals under GCH. For unstable theories, the question: in which cardinals do universals exist in models of failures of GCH, requires more set-theoretic techniques to answer.

The main results are joint work with Sy Friedman.