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Towards the Kechris-Pestov-Todorčević correspondence for projective Fraïssé limits

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Combinatorics; Dynamical systems and ergodic theory; Logic and foundations

video/mp4

Author affiliation: University of Novi Sad, Faculty of Sciences

2016-05-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58119

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/