{"product_id":"the-theory-of-countable-borel-equivalence-relations-hardback-9781009562294","title":"The Theory of Countable Borel Equivalence Relations (Hardback) 9781009562294","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Theory of Countable Borel Equivalence Relations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA survey of the state of the art in a very active area of research in descriptive set theory.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAlexander S. Kechris (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009562294, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 November 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e176 pages\u003cbr\u003e23.9 x 15.9 x 1.3 cm, 0.41 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Equivalence relations and reductions\u003cbr\u003e 2. Countable Borel equivalence relations\u003cbr\u003e 3. Essentially countable relations\u003cbr\u003e 4. Invariant and quasi-invariant measures\u003cbr\u003e 5. Smoothness, $mathbf{E}_0$ and $mathbf{E}_infty$\u003cbr\u003e 6. Rigidity and incomparability\u003cbr\u003e 7. Hyperfiniteness\u003cbr\u003e 8. Amenability\u003cbr\u003e 9. Treeability\u003cbr\u003e 10. Freeness\u003cbr\u003e 11. Universality\u003cbr\u003e 12. The poset of bireducibility types\u003cbr\u003e 13. Structurability\u003cbr\u003e 14. Topological realizations\u003cbr\u003e 15. A universal space for actions and equivalence relations\u003cbr\u003e 16. Open problems\u003cbr\u003e References\u003cbr\u003e List of Notation\u003cbr\u003e Subject Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52515967729944,"sku":"9781009562294","price":82.59,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-theory-of-countable-borel-equivalence-relations-hardback-9781009562294","provider":"Freshly Printed Books","version":"1.0","type":"link"}