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Topological dynamics of automorphism groups of Hrushovski constructions

Banff International Research Station for Mathematical Innovation and Discovery

Using Hrushovski’s predimension construction, we show that there exists a countable, $\omega$-categorical structure $M$ with the property that if $H$ is an extremely amenable subgroup of the automorphism group of $M$, then $H$ has infinitely many orbits on $M^2$. In particular, $H$ is not oligomorphic. This answers a question raised by several authors (including Bodirsky, Pinsker, Tsankov and Ne\v set\v ril). It follows that there is a closed, oligomorphic permutation group $G$ whose universal minimal flow $M(G)$ is not metrizable.

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

video/mp4

Author affiliation: University of East Anglia

2016-05-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58133

Unreviewed

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