Borel Equivalence Relations
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Author | : Vladimir Grigorʹevich Kanoveĭ |
Publisher | : American Mathematical Soc. |
Total Pages | : 254 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821844539 |
"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 | : Greg Hjorth |
Publisher | : American Mathematical Soc. |
Total Pages | : 217 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821820028 |
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. |
Total Pages | : 126 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821837710 |
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 | : Springer Science & Business Media |
Total Pages | : 148 |
Release | : 2004-08-26 |
Genre | : Computers |
ISBN | : 9783540226031 |
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 |
Total Pages | : 392 |
Release | : 2008-09-03 |
Genre | : Mathematics |
ISBN | : 9781584887942 |
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 | : M. Foreman |
Publisher | : Cambridge University Press |
Total Pages | : 304 |
Release | : 2000-05-25 |
Genre | : Mathematics |
ISBN | : 9780521786447 |
This volume, first published in 2000, contains a collection of survey papers providing an introduction for graduate students and researchers in these fields.
Author | : Klaus Schmidt |
Publisher | : American Mathematical Soc. |
Total Pages | : 104 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821889206 |
Author | : James Cummings |
Publisher | : Cambridge University Press |
Total Pages | : 433 |
Release | : 2012-11-15 |
Genre | : Mathematics |
ISBN | : 1107608503 |
Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.
Author | : John Daniel Clemens |
Publisher | : |
Total Pages | : 308 |
Release | : 2001 |
Genre | : |
ISBN | : |
Author | : Howard Becker |
Publisher | : Cambridge University Press |
Total Pages | : 152 |
Release | : 1996-12-05 |
Genre | : Mathematics |
ISBN | : 0521576059 |
In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces.