Alexei Kolesnikov: Hanf number for amalgamation and disjoint amalgamation

Model Theory Seminar
Date: Monday, April 28, 2014
Time: 5:00 pm
Location: Wean 8220, Carnegie Mellon University

Speaker: Alexei Kolesnikov

Title: Hanf number for amalgamation and disjoint amalgamation

Abstract: This is a joint work of Lambie-Hanson and the speaker. We study a family of abstract elementary classes that we call coloring classes. Each coloring class is an AEC in a relational language L containing exactly the L-structures whose finite substructures are isomorphic to one of the “allowed” finite structures. We define an “existence rank” on the set of the allowable finite structures and develop connections between the rank values, the existence of models, and amalgamation properties. This allows us to improve the results of Baldwin, Kolesnikov, and Shelah: we show in ZFC that disjoint amalgamation can hold up to α, α<ω1. We also give a partial answer to the question of Grossberg about the Hanf number for amalgamation property (not just disjoint amalgamation).