Model theory of operator algebras III: elementary equivalence and II1factors

DOI10.1112/blms/bdu012zbMath1303.46049arXiv1111.0998OpenAlexW3101441544MaRDI QIDQ5419248

Bradd Hart, Ilijas Farah, David J. Sherman

Publication date: 6 June 2014

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.0998

zbMATH Keywords

ultrapowersConnes embedding problemcontinuous model theory\({\mathrm {II}}_{1}\) factors

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Ultraproducts and related constructions (03C20) Applications of model theory (03C98) Classification of factors (46L36)

Related Items (26)

Existentially closed \(\mathrm{W}^*\)-probability spaces ⋮ Applications of model theory to \(C^*\)-dynamics ⋮ Malnormal matrices ⋮ Remarks on the diagonal embedding and strong 1-boundedness ⋮ An exotic \(\mathrm{II}_1\) factor without property Gamma ⋮ Existential closedness and the structure of bimodules of \(\mathrm{II}_1\) factors ⋮ Covering entropy for types in tracial W^*-algebras ⋮ Embedding universality for \(\mathrm{II}_1\) factors with property (T) ⋮ On Popa’s factorial commutant embedding problem ⋮ AN INVITATION TO MODEL THEORY AND C*-ALGEBRAS ⋮ ENFORCEABLE OPERATOR ALGEBRAS ⋮ Relative commutants of strongly self-absorbing \(\mathrm{C}^\ast\)-algebras ⋮ Properties expressible in small fragments of the theory of the hyperfinite \(\mathrm{II}_1\) factor ⋮ Independence properties in subalgebras of ultraproduct \(\mathrm{II}_1\) factors ⋮ Ultraproducts of von Neumann algebras ⋮ Existentially closed ${\rm II}_1$ factors ⋮ Convex sets associated to \(C^{\ast}\)-algebras ⋮ Model theory of 𝐶*-algebras ⋮ II₁ FACTORS WITH EXOTIC CENTRAL SEQUENCE ALGEBRAS ⋮ Factorial relative commutants and the generalized Jung property for \(\mathrm{II}_1\) factors ⋮ Continuous model theories for von Neumann algebras ⋮ Model theory and Rokhlin dimension for compact quantum group actions ⋮ CATEGORICAL SEMANTICS OF METRIC SPACES AND CONTINUOUS LOGIC ⋮ On Kirchberg's embedding problem ⋮ Hilbert spaces and \(C^\ast\)-algebras are not finitely concrete ⋮ The Connes embedding problem: A guided tour

Cites Work

• Unnamed Item
• Model theory of operator algebras. II: Model theory
• Pseudofinite and pseudocompact metric structures
• Tracial algebras and an embedding theorem
• Divisible operators in von Neumann algebras
• The finite dimensional basis problem with an appendix on nets of Grassmann manifolds
• On II\(_{1}\) factors arising from 2-cocycles of \(w\)-rigid groups
• On ultraproducts of operator algebras
• The relative commutant of separable C\(^*\)-algebras of real rank zero
• Geometry and probability in Banach spaces. Notes by Paul R. Chernoff
• On a problem of R.V. Kadison on maximal Abelian *-subalgebras in factors
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Nonstandard hulls of Banach spaces
• The analogues of entropy and of Fisher's information measure in free probability theory. II
• Convex sets associated with von Neumann algebras and Connes' approximate embedding problem
• T-property and nonisomorphic full factors of types II and III
• The Effros-Maréchal topology in the space of von Neumann algebras. II
• Uniformly non-square Banach spaces
• Central sequence algebras of von Neumann algebras
• Every two elementarily equivalent models have isomorphic ultrapowers
• A reduction for algebras of finite type
• On rings of operators. IV
• Continuous first order logic and local stability
• A DICHOTOMY FOR THE NUMBER OF ULTRAPOWERS
• LOCALLY INNER AUTOMORPHISMS OF OPERATOR ALGEBRAS
• Notes on automorphisms of ultrapowers of II₁factors
• Langages à valeurs réelles et applications
• Ultrapowers and Local Properties of Banach Spaces
• Free Product Von Neumann Algebras of Type III
• The Effros-Marechal topology in the space of von Neumann algebras
• POSITIVE MODEL THEORY AND COMPACT ABSTRACT THEORIES
• There is no separable universal 𝐼𝐼₁-factor
• ABOUT THE QWEP CONJECTURE
• Application des ultraproduits à l'étude des espaces et des algèbres de Banach
• Model theory of operator algebras I: stability
• Hyperlinear and Sofic Groups: A Brief Guide
• Central Sequences and the Hyperfinite Factor
• Minimal Identities for Algebras
• Approximately finite-dimensional Banach spaces
• Theory of operator algebras I.

This page was built for publication: Model theory of operator algebras III: elementary equivalence and II₁factors