Logic Seminar

Please note that the time is PST

This speaker will present the notion of hyper-u-amenability for countable Borel equivalence relations, a property that implies 1-amenability and which is automatic for orbit equivalence relations of continuous amenable actions on sigma-compact Polish spaces, and for orbit equivalence relations of Borel actions of amenable groups. The speaker will then show that hyper-u-amenable, treeable countable Borel equivalence relations are hyperfinite. As corollaries, the speaker will show that, for orbit equivalence relations of free continuous actions of free groups on sigma-compact spaces, measure-hyperfiniteness implies hyperfiniteness, and that the orbit equivalence relation of a Borel action by an amenable group is hyperfinite, if treeable. The material presented is part of a joint work with Petr Naryshkin.