Authors: Farah, Ilijas 
Toms, Andrew
Törnquist, Asger
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The descriptive set theory of C*-algebra Invariants
Journal: International Mathematics Research Notices
Volume: 2013
Issue: 22
First page: 5196
Last page: 5226
Issue Date: 1-Jan-2013
Rank: M21a
ISSN: 1073-7928
DOI: 10.1093/imrn/rns206
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.
Publisher: Oxford University Press
Project: NSF, Grants DMS-1101144 and DMS-0969246
Denmarks Natural Sciences Research Council, Grant no. 10-082689/FNU
Marie Curie reintegration grant, no. IRG-249167

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