arXiv subjects
Publications and source records attributed to Alexander Berenstein.
Let G be a countable group. We proof that there is a model companion for the approximate theory of a Hilbert space with a group G of automorphisms. We show that G is amenable if and only if the structure induced by countable copies of the regular representation of G is existentially closed.
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic structures of this kind are exactly the ones isomorphic to the measure algebra of a standard Lebesgue space equipped with an aperiodic measure-preserving automorphism. The corresponding theory is complete and has quantifier elimination; moreover it is stable with built-in canonical bases. We give an intrinsic characterization of its independence relation.