Borel Equivalence Relations

Author : Vladimir Grigorʹevich Kanoveĭ
Publisher : American Mathematical Soc.
ISBN 13 : 0821844539
Total Pages : 254 pages
Book Rating : 4.33/5 ( download)

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Download or read book Borel Equivalence Relations written by Vladimir Grigorʹevich Kanoveĭ and published by American Mathematical Soc.. This book was released on 2008 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications."--BOOK JACKET.

Author : Assaf Shani
Publisher :
ISBN 13 :
Total Pages : 96 pages
Book Rating : 4.03/5 ( download)

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Download or read book Borel Equivalence Relations and Symmetric Models written by Assaf Shani and published by . This book was released on 2019 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a relationship between Borel equivalence relations and weak choice principles. Specifically, we show that questions about Borel reducibility and strong ergodicity between equivalence relations which are classifiable by countable structures can be translated to questions about fragments of choice holding in certain symmetric models. We then use tools developed in the '60s and '70s to analyze such symmetric models and solve several problems about Borel equivalence relations. This relationship is explained in Chapter~\ref{chapter:symmetric-models-borel-reducibility}. These techniques are applied to the study of equivalence relations high in the Borel reducibility hierarchy in Chapter~\ref{chapter:jumps-HKL}. In \cite{HKL98} Hjorth, Kechris and Louveau refined the Friedman-Stanley jump hierarchy by defining equivalence relations $\cong^\ast_{\alpha+1,\beta}$, $\beta

Author : Greg Hjorth
Publisher : American Mathematical Soc.
ISBN 13 : 0821820028
Total Pages : 217 pages
Book Rating : 4.25/5 ( download)

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Download or read book Classification and Orbit Equivalence Relations written by Greg Hjorth and published by American Mathematical Soc.. This book was released on 2000 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a coherent theory of the resulting orbit equivalence classes that may allow complete classification by invariants of an indicated form. The book concludes with a criterion for an orbit equivalence relation classifiable by countable structures considered up to isomorphism. This self-contained volume offers a complete treatment of this active area of current research and develops a difficult general theory classifying a class of mathematical objects up to some relevant notion of isomorphism or equivalence.

Author : Greg Hjorth
Publisher : American Mathematical Soc.
ISBN 13 : 0821837710
Total Pages : 126 pages
Book Rating : 4.19/5 ( download)

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Download or read book Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations written by Greg Hjorth and published by American Mathematical Soc.. This book was released on 2005 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.

Author : Alexander S. Kechris
Publisher : Cambridge University Press
ISBN 13 : 9781009562294
Total Pages : 0 pages
Book Rating : 4.90/5 ( download)

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Download or read book The Theory of Countable Borel Equivalence Relations written by Alexander S. Kechris and published by Cambridge University Press. This book was released on 2024-11-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Benjamin David Miller
Publisher :
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.93/5 ( download)

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Download or read book Full Groups, Classification, and Equivalence Relations written by Benjamin David Miller and published by . This book was released on 2004 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander S. Kechris
Publisher : Springer Science & Business Media
ISBN 13 : 9783540226031
Total Pages : 148 pages
Book Rating : 4.36/5 ( download)

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Download or read book Topics in Orbit Equivalence written by Alexander S. Kechris and published by Springer Science & Business Media. This book was released on 2004-08-26 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.

Author : Su Gao
Publisher : CRC Press
ISBN 13 : 9781584887942
Total Pages : 392 pages
Book Rating : 4.4X/5 ( download)

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Download or read book Invariant Descriptive Set Theory written by Su Gao and published by CRC Press. This book was released on 2008-09-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 mathem

Author : Carlos Uzcategui
Publisher :
ISBN 13 :
Total Pages : 238 pages
Book Rating : 4.31/5 ( download)

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Download or read book Smooth Sets for Borel Equivalence Relations and the Covering Property for Sigma-ideals of Compact Sets written by Carlos Uzcategui and published by . This book was released on 1990 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Klaus Schmidt
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889206
Total Pages : 104 pages
Book Rating : 4.06/5 ( download)

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Download or read book Algebraic Ideas in Ergodic Theory written by Klaus Schmidt and published by American Mathematical Soc.. This book was released on with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: