Axiomatizability of the stable rank of C*-algebras
classification
🧮 math.OA
math.LO
keywords
stablerankalgebrasaxiomatizabilityaxiomatizableclassconsequencecontinuous
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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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