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Towards the Kechris-Pestov-Todorčević correspondence for projective Fraïssé limits Masulovic, Dragan

Description

In this talk we present a way to reinterpret the Kechris-Pestov-Todorčević correspondence in an abstract categorical setting. We then instantiate this abstract setting in several ways. The interpretation in the category of countable structrures with embeddings will give us the well-known resutls of K-P-T theory for Fraïssé limits. The interpretation of this setting in categories of arbitrary structures with embeddings yields some recent results of Bartov sova in which extreme anemability of automorphism groups of some uncounable structures was established. Finally, the interpretation in op-categories yields duals of some results of K-P-T theory. For example, we shall show that if $F$ is a projectively homogeneous structure, then $Aut(F)$ is extremely amenable if and only if the projective age of $F$ has the dual Ramsey property.

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Attribution-NonCommercial-NoDerivatives 4.0 International