Chris Lambie-Hanson: Well-colorings and the Hanf number for amalgamation

Infinite Combinatorics Seminar (BIU)

9/November/2014, 10-12,
Room 201, Building 216, Bar-Ilan University

Speaker: Chris Lambie-Hanson (HUJI)

Title: Well-colorings and the Hanf number for amalgamation

Abstract: The amalgamation property is a topic of fundamental interest in model theory and is still imperfectly understood. In the 1980s, Grossberg asked a question, which remains open to this day, about the existence of a Hanf number for amalgamation in abstract elementary classes. We introduce a new class of structures, called well-colorings, and use them to give a partial answer to Grossberg’s question, significantly improving upon previous work of Baldwin, Kolesnikov, and Shelah. We shall start the talk by briefly discussing the relevant model-theoretic definitions (no prior model-theoretic knowledge will be assumed) and will then give proofs of the main results, which are entirely set-theoretic and combinatorial in nature and of interest in their own right. This is joint work with Alexei Kolesnikov.

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