Unitary equivalence of automorphisms of separable C*-algebras

We prove that the automorphisms of any separable C*-algebra that does not have continuous trace are not classifiable by countable structures up to unitary equivalence. This implies a dichotomy for the Borel complexity of the relation of unitary equivalence of automorphisms of a separable unital C*-algebra: Such relation is either smooth or not even classifiable by countable structures.Comment: Submitted for publicatio

An intrinsic order-theoretic characterization of the weak expectation property

We prove the following characterization of the weak expectation property for operator systems in terms of Wittstock's matricial Riesz separation property: an operator system $S$ satisfies the weak expectation property if and only if $M_{q}(S)$ satisfies the matricial Riesz separation property for every $q\in \mathbb{N}$. This can be seen as the noncommutative analog of the characterization of simplex spaces among function systems in terms of the classical Riesz separation property

Logic for metric structures and the number of universal sofic and hyperlinear groups

Using the model theory of metric structures, I give an alternative proof of the following result by Thomas: If the Continuum Hypothesis fails then there are power of the continuum many universal sofic groups up to isomorphism. This method is also applicable to universal hyperlinear groups, giving a positive answer to a question posed by Thomas.Comment: 14 pages; accepted for publication by the Proceedings of the American Mathematical Societ

The classification problem for automorphisms of C*-algebras

We present an overview of the recent developments in the study of the classification problem for automorphisms of C*-algebras from the perspective of Borel complexity theory.Comment: 21 page

Games orbits play and obstructions to Borel reducibility

We introduce a new, game-theoretic approach to anti-classification results for orbit equivalence relations. Within this framework, we give a short conceptual proof of Hjorth's turbulence theorem. We also introduce a new dynamical criterion providing an obstruction to classification by orbits of CLI groups. We apply this criterion to the relation of equality of countable sets of reals, and the relations of unitary conjugacy of unitary and selfadjoint operators on the separable infinite-dimensional Hilbert space.Comment: 13 pages. Final version, to appear in Groups, Geometry, and Dynamic