McMaster-Waterloo Model Theory Seminar

Joey Lakerdas-Gayle, University of Waterloo

Symmetrically indivisible and elementarily indivisible structures

A first order structure M is indivisible if for every colouring of M into two colours, there is a monochromatic substructure N of M that is isomorphic to M. We will consider two stronger properties: M is symmetrically indivisible if N can be chosen so that every automorphism of N extends to an automorphism of M; and M is elementarily indivisible if N can be chosen to be an elementary substructure of M. We will discuss Model-Theoretic methods developed by Kojman and Geschke (2008), Hasson, Kojman, and Onshuus (2009), and Meir (2019) to study the relationships between these notions.

MC 5403