Preservation of elementarity by tensor products of tracial von Neumann algebras

Abstract

Tensoring with type I algebras preserves elementary equivalence in the category of tracial von Neumann algebras. The proof involves a novel and general Feferman--Vaught-type theorem for direct integrals of metric structures.

24 pages. various minor improvements. To appear in Pacific J. Math

Cited by in corpus (2)

• Elementary equivalence and disintegration of tracial von Neumann algebras
• Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras