Norbert Sauer: On partitions of relational structures

Week 2, Wednesday June 24, 09:00-09:50

Partition properties of homogeneous relational structures are determined by their automorphism groups. Hence permutation groups closed in the finitary topology have partition properties, lifted from the partiton properties of the underlying homogeneous structures. Those properties can be defined using permutation group notions only. On the other hand due to results of Kechris, Pestov and Todorcevic and Pestov various connections between actions of topological groups on compacta and relational Ramsey theory have become known.
In order to illustrate various of those partition properties and their interrelationships the simpler case of point partitions will be discussed.