A survey on structural Ramsey theory and topological dynamics with the Kechris-Pestov-Todorcevic correspondence in mind

Abstract

In 2005, Kechris, Pestov and Todorcevic established a surprising correspondence between structural Ramsey theory and topological dynamics. As an immediate consequence, it triggered a new interest for structural Ramsey theory. The purpose of the present paper is to present a self-contained survey of the corresponding developments.

17 pages, survey paper. Caution: The published version of the paper, written in 2013 and submitted in final version in 2014, does not contain updates regarding references or results after July 2013. This current version contains more complete references, but is still far from being exhaustive