Mathematical logic seminar - October 15 2013

Time: 12:00 - 13:20

Room: Wean Hall 7201

Speaker:     Alexei Kolesnikov    
Department of Mathematics
Towson University

Title: Generalized Martin's axiom and disjoint amalgamation

Abstract: In a joint work with Baldwin and Shelah, we construct examples of abstract elementary classes that have the disjoint amalgamation property for models of size up to $\beth_\alpha$, but ultimately failing to have the disjoint amalgamation for sufficiently large models. The argument relies on a set-theoretic principle introduced by Shelah. A form of that principle was used by Shelah to study simple unstable theories.