Model Theory of C^*-Algebras.

Cover
Title page
Chapter 1. Introduction
Chapter 2. Continuous model theory
2.1. Preliminaries
2.2. Theories
2.3. Ultraproducts
2.3.1. Atomic and Elementary Diagrams
2.4. Elementary classes and preservation theorems
2.5. Elementary classes of \cstar-algebras
2.5.1. Abelian algebras
2.5.2. Non-abelian algebras
2.5.3. Real rank zero again
2.5.4. -subhomogeneous
2.5.5. Non- -subhomogeneous algebras
2.5.6. Tracial \cstar-algebras
2.5.7. \cstar-algebras with a character
2.6. Downward Löwenheim-Skolem
2.7. Tensorial absorption and elementary submodels
2.7.1. Strongly self-absorbing \cstar-algebras
2.7.2. Stable algebras
Chapter 3. Definability and ^{\eq}
3.1. Expanding the definition of formula: definable predicates and functions
3.1.1. Definable predicates
3.2. Expanding the definition of formula: definable sets
3.3. Expanding the language: imaginaries
Countable products
Definable sets
Quotients
^{\eq} and ^{\eq}
3.4. The use of continuous functional calculus
3.5. Definability of traces
3.5.1. Definability of Cuntz-Pedersen equivalence
3.6. Axiomatizability via definable sets
3.6.1. Projectionless and unital projectionless
3.6.2. Real rank zero revisited
3.6.3. Infinite \cstar-algebras
3.6.4. Finite and stably finite algebras
3.7. Invertible and non-invertible elements
3.8. Stable rank
3.9. Real rank
3.10. Tensor products
3.11. ₀( ) and ^{\eq}
3.12. ₁( ) and ^{\eq}
3.13. Co-elementarity
3.13.1. Abelian algebras
3.13.2. Infinite algebras
3.13.3. Algebras containing a unital copy of _{ }(\bbC)
3.13.4. Definability of sets of projections
3.13.5. Stable rank one
3.13.6. Real rank zero
3.13.7. Purely infinite simple \cstar-algebras
3.14. Some non-elementary classes of \cstar-algebras.

Chapter 4. Types
4.1. Types: the definition
4.1.1. Types as sets of conditions
4.2. Beth definability
4.3. Saturated models
4.4. MF algebras
4.5. Approximately divisible algebras
Chapter 5. Approximation properties
5.1. Nuclearity
5.2. Completely positive contractive order zero maps
5.3. Nuclear dimension
5.4. Decomposition rank
5.5. Quasidiagonal algebras
5.6. Approximation properties and definability
5.7. Approximation properties and uniform families of formulas
5.7.1. Uniform families of formulas
5.8. Nuclearity, nuclear dimension and decomposition rank: First proof
5.9. Nuclearity, nuclear dimension and decomposition rank: Second proof
5.10. Simple \cstar-algebras
5.11. Popa algebras
5.12. Simple tracially AF algebras
5.13. Quasidiagonality
5.14. An application: Preservation by quotients
5.15. An application: Perturbations
5.16. An application: Preservation by inductive limits
5.17. An application: Borel sets of \cstar-algebras
Chapter 6. Generic \cstar-algebras
6.1. Henkin forcing
6.2. Infinite forcing
6.3. Finite forcing
6.4. ∀∃-axiomatizability and existentially closed structures
6.5. Strongly self-absorbing algebras
6.6. Stably finite, quasidiagonal, and MF algebras
Chapter 7. \cstar-algebras not elementarily equivalent to nuclear \cstar-algebras
7.1. Exact algebras
7.2. Definability of traces: the uniform strong Dixmier property
7.3. Elementary submodels of von Neumann algebras
Chapter 8. The Cuntz semigroup
8.1. Cuntz subequivalence
8.2. Strict comparison of positive elements
8.3. The Toms-Winter conjecture
8.4. Radius of comparison
Appendix A. \cstar-algebras
Bibliography
Index
Back Cover.