Mathematical Logic Seminar

Speaker: Alex Kruckman, Wesleyan University
Title: A categorical Ramsey Property
Abstract:
A class K of finite structures is said to have the Ramsey Property (RP) if it satisfies a natural generalization of the classical finite Ramsey theorem. RP can be easily phrased as a property of the category of structures in K and embeddings between them, so it makes sense for any category C. Under mild hypotheses on C, I will show that C has RP if and only if every contravariant functor from C to the category of compact Hausdorff spaces has a global element (a kind of fixed-point). This point of view provides a unified explanation for the appearance of the Ramsey property in (a) the Kechris-Pestov-Todorčević theorem on extremely amenable topological groups and (b) Scow’s theorem on the existence of generalized indiscernibles in model theory.
Talk will be presented virtually and can be viewed either in Carver 0401 or via https://iastate.zoom.us/j/93127761644.