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 Citations and Data
Attribution-NonCommercial-NoDerivatives 4.0 International