The Theory of Countable Borel Equivalence Relations

2024-11-22 分类：Cambridge 评论(0)

The Theory of Countable Borel Equivalence Relations (Cambridge Tracts in Mathematics, Series Number 234)

The Theory of Countable Borel Equivalence Relations (Cambridge Tracts in Mathematics, Series Number 234)

Author: Alexander S. Kechris (Author)

Publisher finelybook 出版社:‏ Cambridge University Press

Edition 版本:‏ 1st edition

Publication Date 出版日期:‏ 2024-11-21

Language 语言: English

Print Length 页数: 174 pages

ISBN-10: 1009562290

ISBN-13: 9781009562294

Book Description

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.

Book Description

A survey of the state of the art in a very active area of research in descriptive set theory.

About the Author

Alexander S. Kechris is Professor of Mathematics at the California Institute of Technology. He is the recipient of numerous honors, including the Sloan Research Fellowship, the J. S. Guggenheim Memorial Foundation Fellowship, and the Carol Karp Prize of the Association for Symbolic Logic. He is also an Inaugural Fellow of the American Mathematical Society.

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