Logic Seminar - Eugenio Colla

Wed, 30/10/201911:00-13:00
Ross 63
Model-theoretic proofs of partition theorems for semigroups.

Partition theorems have the following form. Let "regular" be some notion for a structure S; theorem: for every finite partition of S there is a "regular" set inside a cell of the partition. 
In this talk, we consider a semigroup S and a monoid M acting on S. The "regular" set can be thought as the span, inside S, of an infinite sequence. In fact, it is often called "combinatorial subspace". The class of S and M for which a partition theorem holds is still unknown, but there are several results about it.
Model theory, in this context, is a useful language to give short and uniform proofs. We will focus on the strategy of the proofs and we will give some more details on the proof of Hales-Jewett theorem. We will assume some basic knowledge of model theory.