Structures with Finite Big Ramsey Degrees within the Framework of Arithmetic
Peter Cholak of Notre Dame :
3 p.m. in 636 SEO
Abstract
This is a survey talk on recent work concerning structures with finite big Ramsey degrees, viewed through the framework of arithmetic. Even the first part of the title—“structures with finite big Ramsey degrees”—takes some unpacking, and we will begin by explaining what this means.
The main theme is that many of the ideas and constructions involved can be formulated within arithmetic, and that the techniques needed to study them can likewise be carried out within arithmetic. We will illustrate this theme through several examples, developing some of the relevant constructions and proofs along the way.