Model Theory of C*-Algebras:
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| Main Authors: | , , , , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence
American Mathematical Society
[2021]
|
| Series: | Memoirs of the American Mathematical Society
volume 271, number 1324 (first of 7 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 127 Seiten |
| ISBN: | 9781470447571 |
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| 100 | 1 | |a Farah, Ilijas |d 1966- |0 (DE-588)173427405 |4 aut | |
| 245 | 1 | 0 | |a Model Theory of C*-Algebras |c Ilijas Farah ; Bradd Hart ; Martino Lupini ; Leonel Robert ; Aaron Tikuisis ; Alessandro Vignati ; Wilhelm Winter |
| 264 | 1 | |a Providence |b American Mathematical Society |c [2021] | |
| 300 | |a viii, 127 Seiten | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 271, number 1324 (first of 7 numbers) | |
| 700 | 1 | |a Hart, Bradd T. |d 1960- |0 (DE-588)1026342716 |4 aut | |
| 700 | 1 | |a Lupini, Martino |0 (DE-588)1080565531 |4 aut | |
| 700 | 1 | |a Robert, Leonel |0 (DE-588)1245490036 |4 aut | |
| 700 | 1 | |a Tikuisis, Aaron |d 1982- |0 (DE-588)1179943724 |4 aut | |
| 700 | 1 | |a Vignati, Alessandro |0 (DE-588)1245578324 |4 aut | |
| 700 | 1 | |a Winter, Wilhelm |d 1968- |0 (DE-588)122275047 |4 aut | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1 Introduction
Chapter 2 Continuous model theory
2 1 Preliminaries
2 2 Theories
2 3 Ultraproducts
231 Atomic and Elementary Diagrams
2 4 Elementary classes and preservation theorems
2 5 Elementary classes of C*-algebras
251 Abelian algebras
252 Non-abelian algebras
253 Real rank zero again
254 n-subhomogeneous
255 Non-n-subhomogeneous algebras
256 Tracial C*-algebras
257 C*-algebras with a character
2 6 Downward Löwenheim-Skolem
2 7 Tensorial absorption and elementary submodels
271 Strongly self-absorbing C*-algebras
272 Stable algebras
Chapter 3 Definability and A®?
3 1 Expanding the definition of formula: definable predicates and
functions
311 Definable predicates
3 2 Expanding the definition of formula: definable sets
3 3 Expanding the language: imaginaries
Countable products
Definable sets
Quotients
M®* and T°4
3 4 The use of continuous functional calculus
3 5 Definability of traces
351 Definability of Cuntz-Pedersen equivalence
3 6 Axiomatizability via definable sets
361 Projectionless and unital projectionless
362 Real rank zero revisited
363 Infinite C*-algebras
364 Finite and stably finite algebras
3 7 Invertible and non-invertible elements
iii
4l
Al
CONTENTS
3 8 Stable rank
3 9 Real rank
Tensor products
Ko(A) and A°“
Kı(A) and A®a
Co-elementarity
Abelian algebras
Infinite algebras
Algebras containing a unital copy of M,(C)
Definability of sets of projections
Stable rank one
Real rank zero
Purely infinite simple C*-algebras
Some non-elementary classes of C*-algebras
Chapter 4 Types
4 1 Types: the definition
4 A
Types as sets of conditions
Beth definability
Saturated models
MF algebras
Approximately divisible algebras
Chapter 5 Approximation properties
Nuclearity
Completely positive contractive order zero maps
Nuclear dimension
Decomposition rank
Quasidiagonal algebras
Approximation properties and definability
Approximation properties and uniform families of formulas
Uniform families of formulas
Nuclearity, nuclear dimension and decomposition rank: First proof
Nuclearity, nuclear dimension and decomposition rank: Second proof
Simple C*-algebras
Popa algebras
Simple tracially AF algebras
Quasidiagonality
An application: Preservation by quotients
An application: Perturbations
An application: Preservation by inductive limits
An application: Borel sets of C*-algebras
Chapter 6 Generic C*-algebras
Henkin forcing
Infinite forcing
Finite forcing
V3-axiomatizability and existentially closed structures
Strongly self-absorbing algebras
CONTENTS
6 6 Stably finite, quasidiagonal, and MF algebras
Chapter 7 C*-algebras not elementarily equivalent to nuclear C*-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 C*-algebras
Bibliography
Index
|
| adam_txt |
Contents
Chapter 1 Introduction
Chapter 2 Continuous model theory
2 1 Preliminaries
2 2 Theories
2 3 Ultraproducts
231 Atomic and Elementary Diagrams
2 4 Elementary classes and preservation theorems
2 5 Elementary classes of C*-algebras
251 Abelian algebras
252 Non-abelian algebras
253 Real rank zero again
254 n-subhomogeneous
255 Non-n-subhomogeneous algebras
256 Tracial C*-algebras
257 C*-algebras with a character
2 6 Downward Löwenheim-Skolem
2 7 Tensorial absorption and elementary submodels
271 Strongly self-absorbing C*-algebras
272 Stable algebras
Chapter 3 Definability and A®?
3 1 Expanding the definition of formula: definable predicates and
functions
311 Definable predicates
3 2 Expanding the definition of formula: definable sets
3 3 Expanding the language: imaginaries
Countable products
Definable sets
Quotients
M®* and T°4
3 4 The use of continuous functional calculus
3 5 Definability of traces
351 Definability of Cuntz-Pedersen equivalence
3 6 Axiomatizability via definable sets
361 Projectionless and unital projectionless
362 Real rank zero revisited
363 Infinite C*-algebras
364 Finite and stably finite algebras
3 7 Invertible and non-invertible elements
iii
4l
Al
CONTENTS
3 8 Stable rank
3 9 Real rank
Tensor products
Ko(A) and A°“
Kı(A) and A®a
Co-elementarity
Abelian algebras
Infinite algebras
Algebras containing a unital copy of M,(C)
Definability of sets of projections
Stable rank one
Real rank zero
Purely infinite simple C*-algebras
Some non-elementary classes of C*-algebras
Chapter 4 Types
4 1 Types: the definition
4 A
Types as sets of conditions
Beth definability
Saturated models
MF algebras
Approximately divisible algebras
Chapter 5 Approximation properties
Nuclearity
Completely positive contractive order zero maps
Nuclear dimension
Decomposition rank
Quasidiagonal algebras
Approximation properties and definability
Approximation properties and uniform families of formulas
Uniform families of formulas
Nuclearity, nuclear dimension and decomposition rank: First proof
Nuclearity, nuclear dimension and decomposition rank: Second proof
Simple C*-algebras
Popa algebras
Simple tracially AF algebras
Quasidiagonality
An application: Preservation by quotients
An application: Perturbations
An application: Preservation by inductive limits
An application: Borel sets of C*-algebras
Chapter 6 Generic C*-algebras
Henkin forcing
Infinite forcing
Finite forcing
V3-axiomatizability and existentially closed structures
Strongly self-absorbing algebras
CONTENTS
6 6 Stably finite, quasidiagonal, and MF algebras
Chapter 7 C*-algebras not elementarily equivalent to nuclear C*-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 C*-algebras
Bibliography
Index |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:34:16Z |
| indexdate | 2024-07-10T09:15:32Z |
| institution | BVB |
| isbn | 9781470447571 |
| language | English |
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| physical | viii, 127 Seiten |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Farah, Ilijas 1966- (DE-588)173427405 aut Model Theory of C*-Algebras Ilijas Farah ; Bradd Hart ; Martino Lupini ; Leonel Robert ; Aaron Tikuisis ; Alessandro Vignati ; Wilhelm Winter Providence American Mathematical Society [2021] viii, 127 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 271, number 1324 (first of 7 numbers) Hart, Bradd T. 1960- (DE-588)1026342716 aut Lupini, Martino (DE-588)1080565531 aut Robert, Leonel (DE-588)1245490036 aut Tikuisis, Aaron 1982- (DE-588)1179943724 aut Vignati, Alessandro (DE-588)1245578324 aut Winter, Wilhelm 1968- (DE-588)122275047 aut Memoirs of the American Mathematical Society volume 271, number 1324 (first of 7 numbers) (DE-604)BV008000141 1324 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032969743&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farah, Ilijas 1966- Hart, Bradd T. 1960- Lupini, Martino Robert, Leonel Tikuisis, Aaron 1982- Vignati, Alessandro Winter, Wilhelm 1968- Model Theory of C*-Algebras Memoirs of the American Mathematical Society |
| title | Model Theory of C*-Algebras |
| title_auth | Model Theory of C*-Algebras |
| title_exact_search | Model Theory of C*-Algebras |
| title_exact_search_txtP | Model Theory of C*-Algebras |
| title_full | Model Theory of C*-Algebras Ilijas Farah ; Bradd Hart ; Martino Lupini ; Leonel Robert ; Aaron Tikuisis ; Alessandro Vignati ; Wilhelm Winter |
| title_fullStr | Model Theory of C*-Algebras Ilijas Farah ; Bradd Hart ; Martino Lupini ; Leonel Robert ; Aaron Tikuisis ; Alessandro Vignati ; Wilhelm Winter |
| title_full_unstemmed | Model Theory of C*-Algebras Ilijas Farah ; Bradd Hart ; Martino Lupini ; Leonel Robert ; Aaron Tikuisis ; Alessandro Vignati ; Wilhelm Winter |
| title_short | Model Theory of C*-Algebras |
| title_sort | model theory of c algebras |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032969743&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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