Logic Seminar

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Let Γ be a countable free group. The set of continuous actions of Γ on Cantor space 2^N admits a natural Polish topology, and hence we can talk about properties of the generic action. It was shown by Frisch-Kechris-Shinko-Vidnyánszky that the generic action is measure-hyperfinite, meaning that for every Borel probability measure μ on 2^N, the action is hyperfinite modulo some μ-null set. Kwiatkowska showed using the methods of projective Fraïssé theory that there is only one generic action up to isomorphism. We use her techniques to investigate the generic action further, and in particular we show that the generic action is hyperfinite. This is joint work with Sumun Iyer.