### 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.