Invariant Descriptive Set Theory
Language: English
Published by Taylor & Francis Ltd (Sales) Sep 2008, 2008
Series: Book 40 of 70 - Chapman & Hall/CRC Pure and Applied Mathematics
- Hardcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
£ 352.53
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Add to basketItem description from seller
Neuware - Presents Results from a Very Active Area of ResearchExploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields.After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm-Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.…
Seller Inventory # 9781584887935
- Title
- Invariant Descriptive Set Theory
- Author
- Su Gao
- Publisher
- Taylor & Francis Ltd (Sales) Sep 2008
- Publication year
- 2008
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 1584887931
- ISBN 13
- 9781584887935
- Item weight
- 680 grams
- Dimensions
- 236x155x25 mm
- Series
- Book 40 of 70: Chapman & Hall/CRC Pure and Applied Mathematics
Presents Results from a Very Active Area of Research
Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields.
After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations.
By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.
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