Model theory of operator algebras II: model theory
By Ilijas Farah, Bradd Hart, David Sherman. 2010
188 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f71c8dad62099f9b6b0b574d7b358af863182e06
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In Algebra and Number Theory
- Selccuk Barlak
- Thomas Sinclair
- Isaac Goldbring
- G'abor Szab'o
- Gilles Pisier
- Adrian Ioana
- Marius Junge
In Geometry and Topology
In Mathematical Physics
- Selccuk Barlak
- Thomas Sinclair
- Isaac Goldbring
- G'abor Szab'o
- Gilles Pisier
- Marius Junge
- Adrian Ioana
- Assaf Naor
Citations in the corpus
- Tensor Products of C*-Algebras and Operator Spaces (2020, background): “See [86, 87, 88, 89] where the analogous question for ultraproducts of (Mn)n≥1 is discussed as well as other similar issues.”
- On Kirchberg's Embedding Problem (2014, background): “x)) ≥ r+ ǫ 2 . Appendix B. Operator spaces and systems in continuous logic We first show how to axiomatize operator systems in continuous logic. We work in the version of continuous logic presented in [12]. We think of an operator system as a many sorted structure with sorts: 36 ISAAC GOLDBRING AND T”
- Sequentially split ∗-homomorphisms between C*-algebras (2015, background): “As this would require recalling more machinery from [17, 22], we omit the proof for the sake of brevity.”