BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Topological dynamics of automorphism groups of Hrushovski constructions Evans, David


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.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International