The descriptive set theory of C*-algebra Invariants

Abstract

We establish the Borel computability of various C*-algebra invariants, including the Elliott invariant and the Cuntz semigroup. As applications, we deduce that AF algebras are classifiable by countable structures, and that a conjecture of Winter and the second author for nuclear separable simple C*-algebras cannot be disproved by appealing to known standard Borel structures on these algebras.