Axiomatizability of the stable rank of C*-algebras

2016/11/25 by Farah, Ilijas, Rørdam, Mikael
#FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1611.08462

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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