Model theory of operator algebras I: Stability

Abstract

Several authors have considered whether the ultrapower and the relative commutant of a C*-algebra or II_1 factor depend on the choice of the ultrafilter. We settle each of these questions, extending results of Ge-Hadwin and the first author.

15 pages; v3 - some rewriting

Cited by in corpus (9)

• Model theory of operator algebras III: Elementary equivalence and II_1 factors
• II_1 factors with non-isomorphic ultrapowers
• Rigidity of continuous quotients
• A new bicommutant theorem
• ${\aleph }_0$-categorical Banach spaces contain ${\ell }_p$ or $c_0$
• Games and elementary equivalence of $\mathrm{I}{\mathrm{I}}_1$ factors
• Preservation of elementarity by tensor products of tracial von Neumann algebras
• Elementary equivalence and disintegration of tracial von Neumann algebras
• Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras