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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture [[electronic resource] /] / by Valerio Capraro, Martino Lupini
| Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture [[electronic resource] /] / by Valerio Capraro, Martino Lupini |
| Autore | Capraro Valerio |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (VIII, 151 p.) |
| Disciplina | 512.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Group theory
Operator theory Group Theory and Generalizations Operator Theory |
| ISBN | 3-319-19333-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Sofic and hyperlinear groups -- Connes' embedding conjecture -- Conclusions. |
| Record Nr. | UNISA-996466638503316 |
Capraro Valerio
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture / / by Valerio Capraro, Martino Lupini
| Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture / / by Valerio Capraro, Martino Lupini |
| Autore | Capraro Valerio |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (VIII, 151 p.) |
| Disciplina | 512.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Group theory
Operator theory Group Theory and Generalizations Operator Theory |
| ISBN | 3-319-19333-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Sofic and hyperlinear groups -- Connes' embedding conjecture -- Conclusions. |
| Record Nr. | UNINA-9910134931103321 |
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Capraro Valerio
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Model theory of C∗-algebras / / Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, Wilhelm Winter
| Model theory of C∗-algebras / / Ilijas Farah, Bradd Hart, Martino Lupini, Leonel Robert, Aaron Tikuisis, Alessandro Vignati, Wilhelm Winter |
| Autore | Farah Ilijas |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2021 |
| Descrizione fisica | 1 online resource (142 pages) |
| Disciplina | 512/.556 |
| Altri autori (Persone) |
HartBradd
LupiniMartino |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
C*-algebras
Model theory |
| ISBN |
9781470466268
1470466260 |
| Classificazione | 46L0546L3503C2003C9803E1503C25 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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. |
| Record Nr. | UNINA-9910953751803321 |
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Farah Ilijas
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| Providence : , : American Mathematical Society, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory [[electronic resource] /] / by Mauro Di Nasso, Isaac Goldbring, Martino Lupini
| Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory [[electronic resource] /] / by Mauro Di Nasso, Isaac Goldbring, Martino Lupini |
| Autore | Di Nasso Mauro |
| Edizione | [1st ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (XVI, 206 p. 2 illus.) |
| Disciplina | 511.66 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Combinatorics
Mathematical logic Mathematical Logic and Foundations |
| ISBN | 3-030-17956-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466378103316 |
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Di Nasso Mauro
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory / / by Mauro Di Nasso, Isaac Goldbring, Martino Lupini
| Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory / / by Mauro Di Nasso, Isaac Goldbring, Martino Lupini |
| Autore | Di Nasso Mauro |
| Edizione | [1st ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (XVI, 206 p. 2 illus.) |
| Disciplina |
511.66
511.6 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Combinatorial analysis
Logic, Symbolic and mathematical Combinatorics Mathematical Logic and Foundations |
| ISBN | 3-030-17956-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910338257603321 |
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Di Nasso Mauro
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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