# Alexei Kolesnikov: Generalized Martin’s axiom and disjoint amalgamation

The CMU mathematical logic seminar will meet tomorrow
12:00-1:30 in Wean Hall 7201.

Note to newcomers: Seminar follows a “brown bag lunch” format and for
the first ten minutes or so we chat and have lunch. The actual
talk usually runs 12:10-1:20 or so.

Speaker:
Alexei Kolesnikov (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.