Axiomatizability of the stable rank of C*-algebras
  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. 
Ilijas Farah, Mikael R{\o}rdam
math.OA math.LO