The descriptive set theory of Polish group actions /:
In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as g...
Gespeichert in:
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Cambridge University Press,
1996.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
232. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces. |
| Beschreibung: | 1 online resource (136 pages) |
| Bibliographie: | Includes bibliographical references (pages 122-131) and index. |
| ISBN: | 9781107362468 1107362466 |
Internformat
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| 520 | |a In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces. | ||
| 505 | 8 | |a 3.4 The Glimm-Effros Dichotomy3.5 Universal equivalence relations; 4. INVARIANT MEASURES AND PARADOXICAL DECOMPOSITIONS; 4.1 Tarski's Theorem; 4.2 Countable decompositions; 4.3 Nadkarni's Theorem; 4.4 Proof of 4.2.1; 4.5 Sketch of proof of Nadkarni's Theorem; 4.6 Concluding remarks and problems; 5. BETTER TOPOLOGIES; 5.1 Finer topologies and Borel sets; 5.2 Topological realization of Borel G-spaces; 5.3 Topological realization of definable G-spaces; 5.4 Finer topologies on G-spaces; 6. MODEL THEORY AND THE VAUGHT CONJECTURE; 6.1 Background on the Vaught Conjecture | |
| 505 | 8 | |a 6.2 The Topological Vaught Conjecture6.3 Atomic models; 7. ACTIONS WITH BOREL ORBIT EQUIVALENCE RELATIONS; 7.1 Characterizations; 7.2 Some effective considerations; 7.3 Decompositions; 7.4 Tame groups; 7.5 Normalizers; 8. DEFINABLE CARDINALITY; 8.1 Orbit cardinality; 8.2 Orbit cardinality for specific groups; References; Index | |
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| contents | 3.4 The Glimm-Effros Dichotomy3.5 Universal equivalence relations; 4. INVARIANT MEASURES AND PARADOXICAL DECOMPOSITIONS; 4.1 Tarski's Theorem; 4.2 Countable decompositions; 4.3 Nadkarni's Theorem; 4.4 Proof of 4.2.1; 4.5 Sketch of proof of Nadkarni's Theorem; 4.6 Concluding remarks and problems; 5. BETTER TOPOLOGIES; 5.1 Finer topologies and Borel sets; 5.2 Topological realization of Borel G-spaces; 5.3 Topological realization of definable G-spaces; 5.4 Finer topologies on G-spaces; 6. MODEL THEORY AND THE VAUGHT CONJECTURE; 6.1 Background on the Vaught Conjecture 6.2 The Topological Vaught Conjecture6.3 Atomic models; 7. ACTIONS WITH BOREL ORBIT EQUIVALENCE RELATIONS; 7.1 Characterizations; 7.2 Some effective considerations; 7.3 Decompositions; 7.4 Tame groups; 7.5 Normalizers; 8. DEFINABLE CARDINALITY; 8.1 Orbit cardinality; 8.2 Orbit cardinality for specific groups; References; Index |
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| id | ZDB-4-EBA-ocn836871719 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:17Z |
| institution | BVB |
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| spelling | Becker, Howard. The descriptive set theory of Polish group actions / Howard Becker, Alexander S. Kechris. New York : Cambridge University Press, 1996. 1 online resource (136 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 232 Includes bibliographical references (pages 122-131) and index. Print version record. In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces. 3.4 The Glimm-Effros Dichotomy3.5 Universal equivalence relations; 4. INVARIANT MEASURES AND PARADOXICAL DECOMPOSITIONS; 4.1 Tarski's Theorem; 4.2 Countable decompositions; 4.3 Nadkarni's Theorem; 4.4 Proof of 4.2.1; 4.5 Sketch of proof of Nadkarni's Theorem; 4.6 Concluding remarks and problems; 5. BETTER TOPOLOGIES; 5.1 Finer topologies and Borel sets; 5.2 Topological realization of Borel G-spaces; 5.3 Topological realization of definable G-spaces; 5.4 Finer topologies on G-spaces; 6. MODEL THEORY AND THE VAUGHT CONJECTURE; 6.1 Background on the Vaught Conjecture 6.2 The Topological Vaught Conjecture6.3 Atomic models; 7. ACTIONS WITH BOREL ORBIT EQUIVALENCE RELATIONS; 7.1 Characterizations; 7.2 Some effective considerations; 7.3 Decompositions; 7.4 Tame groups; 7.5 Normalizers; 8. DEFINABLE CARDINALITY; 8.1 Orbit cardinality; 8.2 Orbit cardinality for specific groups; References; Index Polish spaces (Mathematics) http://id.loc.gov/authorities/subjects/sh91000874 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Espaces polonais (Mathématiques) Théorie des ensembles. MATHEMATICS Topology. bisacsh Polish spaces (Mathematics) fast Set theory fast Verzamelingen (wiskunde) gtt Lokaal compacte groepen. gtt Espaces polonais. ram Ensembles, Théorie des. ram Kechris, A. S., 1946- https://id.oclc.org/worldcat/entity/E39PBJbxByVfqbvT8tPfHf4cyd http://id.loc.gov/authorities/names/n78076068 Print version: Becker, Howard. Descriptive set theory of Polish group actions. New York : Cambridge University Press, 1996 0521576059 (DLC) 96011786 (OCoLC)34409827 London Mathematical Society lecture note series ; 232. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552380 Volltext |
| spellingShingle | Becker, Howard The descriptive set theory of Polish group actions / London Mathematical Society lecture note series ; 3.4 The Glimm-Effros Dichotomy3.5 Universal equivalence relations; 4. INVARIANT MEASURES AND PARADOXICAL DECOMPOSITIONS; 4.1 Tarski's Theorem; 4.2 Countable decompositions; 4.3 Nadkarni's Theorem; 4.4 Proof of 4.2.1; 4.5 Sketch of proof of Nadkarni's Theorem; 4.6 Concluding remarks and problems; 5. BETTER TOPOLOGIES; 5.1 Finer topologies and Borel sets; 5.2 Topological realization of Borel G-spaces; 5.3 Topological realization of definable G-spaces; 5.4 Finer topologies on G-spaces; 6. MODEL THEORY AND THE VAUGHT CONJECTURE; 6.1 Background on the Vaught Conjecture 6.2 The Topological Vaught Conjecture6.3 Atomic models; 7. ACTIONS WITH BOREL ORBIT EQUIVALENCE RELATIONS; 7.1 Characterizations; 7.2 Some effective considerations; 7.3 Decompositions; 7.4 Tame groups; 7.5 Normalizers; 8. DEFINABLE CARDINALITY; 8.1 Orbit cardinality; 8.2 Orbit cardinality for specific groups; References; Index Polish spaces (Mathematics) http://id.loc.gov/authorities/subjects/sh91000874 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Espaces polonais (Mathématiques) Théorie des ensembles. MATHEMATICS Topology. bisacsh Polish spaces (Mathematics) fast Set theory fast Verzamelingen (wiskunde) gtt Lokaal compacte groepen. gtt Espaces polonais. ram Ensembles, Théorie des. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh91000874 http://id.loc.gov/authorities/subjects/sh85120387 |
| title | The descriptive set theory of Polish group actions / |
| title_auth | The descriptive set theory of Polish group actions / |
| title_exact_search | The descriptive set theory of Polish group actions / |
| title_full | The descriptive set theory of Polish group actions / Howard Becker, Alexander S. Kechris. |
| title_fullStr | The descriptive set theory of Polish group actions / Howard Becker, Alexander S. Kechris. |
| title_full_unstemmed | The descriptive set theory of Polish group actions / Howard Becker, Alexander S. Kechris. |
| title_short | The descriptive set theory of Polish group actions / |
| title_sort | descriptive set theory of polish group actions |
| topic | Polish spaces (Mathematics) http://id.loc.gov/authorities/subjects/sh91000874 Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Espaces polonais (Mathématiques) Théorie des ensembles. MATHEMATICS Topology. bisacsh Polish spaces (Mathematics) fast Set theory fast Verzamelingen (wiskunde) gtt Lokaal compacte groepen. gtt Espaces polonais. ram Ensembles, Théorie des. ram |
| topic_facet | Polish spaces (Mathematics) Set theory. Espaces polonais (Mathématiques) Théorie des ensembles. MATHEMATICS Topology. Set theory Verzamelingen (wiskunde) Lokaal compacte groepen. Espaces polonais. Ensembles, Théorie des. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552380 |
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