Logic Seminar

It is well-known that every non-Archimedean Polish group is Borel isomorphic to the automorphism group of a countable structure, and analogously, that every Polish group is Borel isomorphic to the automorphism group of a separable metric structure. We will present a generalization of this result: every open locally Polish groupoid admits a full and faithful Borel functor to the groupoid of metric L-structures on the Urysohn sphere, for some countable metric language L. This partially answers a question of Lupini. We will also discuss the analogous result in the non-Archimedean case.