# Chris Lambie-Hanson: Coloring classes and the Hanf number for amalgamation.

Set Theory and Topology seminar (BGU)
Notice the one-time change in place to +201.

Time: Tuesday, March 24, 12:15-13:40.
Place: Seminar room +201, Math building 58.
Speaker: Chris Lambie-Hanson (HUJI).
Title: Coloring classes and the Hanf number for amalgamation.
Abstract: The amalgamation property is a topic of fundamental importance in model theory and is still imperfectly understood. In the 1980s, Grossberg asked a question, which remains open, about the existence of a Hanf number for amalgamation in abstract elementary classes. In particular, Grossberg conjectured that the Hanf number for amalgamation for classes given by an $L_{\omega_1, \omega}$ sentence is $beth_{omega_1}$. We introduce a new collection of abstract elementary classes, called coloring classes, and use them to give a partial answer to Grossberg’s question, significantly improving upon work of Baldwin, Kolesnikov, and Shelah. Analysis of these coloring classes leads to some purely combinatorial questions that are of interest in their own right. This is joint work with Alexei Kolesnikov.