The theory of countable Borel equivalence relations:
The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated by the study of group actions in a descriptiv...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2025
|
| Schriftenreihe: | Cambridge tracts in mathematics
234 |
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-634 DE-92 Volltext |
| Zusammenfassung: | The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated by the study of group actions in a descriptive, topological, or measure-theoretic context. A key part of this theory is concerned with the structure of countable Borel equivalence relations. These are exactly the equivalence relations generated by Borel actions of countable discrete groups and this introduces important connections with group theory, dynamical systems, and operator algebras. This text surveys the state of the art in the theory of countable Borel equivalence relations and delineates its future directions and challenges. It gives beginning graduate students and researchers a bird's-eye view of the subject, with detailed references to the extensive literature provided for further study |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 07 Nov 2024) |
| Beschreibung: | 1 Online-Ressource (xiii, 161 Seiten) |
| ISBN: | 9781009562256 |
| DOI: | 10.1017/9781009562256 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2025-01-07T15:01:14Z |
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| isbn | 9781009562256 |
| language | English |
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| spelling | Kechris, Alexander S. 1946- (DE-588)109300025 aut The theory of countable Borel equivalence relations Alexander S. Kechris, California Institute of Technology Cambridge Cambridge University Press 2025 1 Online-Ressource (xiii, 161 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 234 Title from publisher's bibliographic system (viewed on 07 Nov 2024) The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated by the study of group actions in a descriptive, topological, or measure-theoretic context. A key part of this theory is concerned with the structure of countable Borel equivalence relations. These are exactly the equivalence relations generated by Borel actions of countable discrete groups and this introduces important connections with group theory, dynamical systems, and operator algebras. This text surveys the state of the art in the theory of countable Borel equivalence relations and delineates its future directions and challenges. It gives beginning graduate students and researchers a bird's-eye view of the subject, with detailed references to the extensive literature provided for further study Equivalence relations (Set theory) Equivalence classes (Set theory) Borel sets Erscheint auch als Druck-Ausgabe 9781009562294 https://doi.org/10.1017/9781009562256?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kechris, Alexander S. 1946- The theory of countable Borel equivalence relations Equivalence relations (Set theory) Equivalence classes (Set theory) Borel sets |
| title | The theory of countable Borel equivalence relations |
| title_auth | The theory of countable Borel equivalence relations |
| title_exact_search | The theory of countable Borel equivalence relations |
| title_full | The theory of countable Borel equivalence relations Alexander S. Kechris, California Institute of Technology |
| title_fullStr | The theory of countable Borel equivalence relations Alexander S. Kechris, California Institute of Technology |
| title_full_unstemmed | The theory of countable Borel equivalence relations Alexander S. Kechris, California Institute of Technology |
| title_short | The theory of countable Borel equivalence relations |
| title_sort | the theory of countable borel equivalence relations |
| topic | Equivalence relations (Set theory) Equivalence classes (Set theory) Borel sets |
| topic_facet | Equivalence relations (Set theory) Equivalence classes (Set theory) Borel sets |
| url | https://doi.org/10.1017/9781009562256?locatt=mode:legacy |
| work_keys_str_mv | AT kechrisalexanders thetheoryofcountableborelequivalencerelations |