The descriptive set theory of C∗-algebra invariants

TY - JOUR

T1 - The descriptive set theory of C∗-algebra invariants

AU - Farah, Ilijas

AU - Toms, Andrew

AU - Törnquist, Asger Dag

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

U2 - 10.1093/imrn/rns206

DO - 10.1093/imrn/rns206

M3 - Journal article

SN - 1073-7928

VL - 2013

SP - 5196

EP - 5226

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 22

ER -