Model theory of operator algebras II: Model theory

Ilijas Farah, Bradd Hart, David Sherman

Published 2010-04-06, updated 2013-07-14Version 5

We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on N are isomorphic even when the Continuum Hypothesis fails.