Axiomatizability of the stable rank of C*-algebras

Published 25 Nov 2016 in math.OA and math.LO | (1611.08462v2)

Abstract: We show that the class of C*-algebras with stable rank greater than a given positive integer is axiomatizable in logic of metric structures. As a consequence we show that the stable rank is continuous with respect to forming ultrapowers of C*-algebras, and that stable rank is Kadison--Kastler stable.

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