Logic Seminar

The Central Sets Theorem is a Ramsey-theoretic result due to Furstenberg, from 1981, and multiple generalizations of it (in a variety of different directions) have been proved afterwards (to the best of my knowledge, the currently most general statement is due to De, Hindman and Strauss in 2008, but there are also many relevant results due to Bergelson). In this series of two talks, we will explain how to interpret the Central Sets Theorem as a statement about linear polynomials in a polynomial ring with countably many variables, and prove a couple of natural generalizations involving polynomials of higher degree. In order to make this exposition self-contained, we will spend most of the first talk providing an overview of the techniques from algebra in the Cech--Stone compactification, which is the main tool that we use in our proof. Speaker(s): David Fernandez-Breton (University of Michigan)