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Borel Equivalence Relations
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Book Synopsis Borel Equivalence Relations by : Vladimir Grigorʹevich Kanoveĭ
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.
Book Synopsis Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations by : Greg Hjorth
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 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is both a contribution to the theory of Borel equivalence relations, considered up to Borel reducibility, and measure preserving group actions considered up to orbit equivalence. Here $E$ is said to be Borel reducible to $F$ if there is a Borel function $f$ with $x E y$ if and only if $f(x) F f(y)$. Moreover, $E$ is orbit equivalent to $F$ if the respective measure spaces equipped with the extra structure provided by the equivalence relations are almost everywhere isomorphic. We consider product groups acting ergodically and by measure preserving transformations on standard Borel probability spaces.In general terms, the basic parts of the monograph show that if the groups involved have a suitable notion of 'boundary' (we make this precise with the definition of near hyperbolic), then one orbit equivalence relation can only be Borel reduced to another if there is some kind of algebraic resemblance between the product groups and coupling of the action. This also has consequence for orbit equivalence. In the case that the original equivalence relations do not have non-trivial almost invariant sets, the techniques lead to relative ergodicity results. An equivalence relation $E$ is said to be relatively ergodic to $F$ if any $f$ with $xEy \Rightarrow f(x) F f(y)$ has $[f(x)]_F$ constant almost everywhere.This underlying collection of lemmas and structural theorems is employed in a number of different ways. In the later parts of the paper, we give applications of the theory to specific cases of product groups. In particular, we catalog the actions of products of the free group and obtain additional rigidity theorems and relative ergodicity results in this context. There is a rather long series of appendices, whose primary goal is to give the reader a comprehensive account of the basic techniques. But included here are also some new results. For instance, we show that the Furstenberg-Zimmer lemma on cocycles from amenable groups fails with respect to Baire category, and use this to answer a question of Weiss. We also present a different proof that $F_2$ has the Haagerup approximation property.
Book Synopsis Classification and Orbit Equivalence Relations by : Greg Hjorth
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.
Book Synopsis Descriptive Set Theory and Dynamical Systems by : M. Foreman
Download or read book Descriptive Set Theory and Dynamical Systems written by M. Foreman and published by Cambridge University Press. This book was released on 2000-05-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, first published in 2000, contains a collection of survey papers providing an introduction for graduate students and researchers in these fields.
Book Synopsis Algebraic Ideas in Ergodic Theory by : Klaus Schmidt
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:
Book Synopsis Topics in Orbit Equivalence by : Alexander Kechris
Download or read book Topics in Orbit Equivalence written by Alexander Kechris and published by Springer. This book was released on 2004-09-08 with total page 144 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 :Alexander S. Kechris Publisher :Springer Science & Business Media ISBN 13 :9783540226031 Total Pages :148 pages Book Rating :4.2/5 (26 download)
Book Synopsis Topics in Orbit Equivalence by : Alexander S. Kechris
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.
Book Synopsis The Theory of Countable Borel Equivalence Relations by : Alexander S. Kechris
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.
Book Synopsis Classical and New Paradigms of Computation and their Complexity Hierarchies by : Benedikt Löwe
Download or read book Classical and New Paradigms of Computation and their Complexity Hierarchies written by Benedikt Löwe and published by Springer Science & Business Media. This book was released on 2007-11-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.
Book Synopsis Group Colorings and Bernoulli Subflows by : Su Gao
Download or read book Group Colorings and Bernoulli Subflows written by Su Gao and published by American Mathematical Soc.. This book was released on 2016-04-26 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.
Book Synopsis Invariant Descriptive Set Theory by : Su Gao
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
Book Synopsis Appalachian Set Theory by : James Cummings
Download or read book Appalachian Set Theory written by James Cummings and published by Cambridge University Press. This book was released on 2012-11-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers based on a series of workshops where prominent researchers present exciting developments in set theory to a broad audience.
Book Synopsis Proceedings of the 12th Asian Logic Conference by : Rod Downey
Download or read book Proceedings of the 12th Asian Logic Conference written by Rod Downey and published by World Scientific. This book was released on 2013-05-07 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Asian Logic Conference is the most significant logic meeting outside of North America and Europe, and this volume represents work presented at, and arising from the 12th meeting. It collects a number of interesting papers from experts in the field. It covers many areas of logic. Contents:Resolute Sequences in Initial Segment Complexity (G Barmpalias and R G Downey)Approximating Functions and Measuring Distance on a Graph (W Calvert, R Miller and J Chubb Reimann)Carnap and McKinsey: Topics in the Pre-History of Possible-Worlds Semantics (M J Cresswell)Limits to Joining with Generics and Randoms (A R Day and D D Dzhafarov)Freedom & Consistency (M Detlefsen)A van Lambalgen Theorem for Demuth Randomness (D Diamondstone, N Greenberg and D Turetsky)Faithful Representations of Polishable Ideals (S Gao)Further Thoughts on Definability in the Urysohn Sphere (I Goldbring)Simple Completeness Proofs for Some Spatial Logics of the Real Line (I Hodkinson)On a Question of Csima on Computation-Time Domination (X Hua, J Liu and G Wu)A Generalization of Beth Model to Functionals of High Types (F Kachapova)A Computational Framework for the Study of Partition Functions and Graph Polynomials (T Kotek, J A Makowsky and E V Ravve)Relation Algebras and R (T Kowalski)Van Lambalgen's Theorem for Uniformly Relative Schnorr and Computable Randomness (K Miyabe and J Rute)Computational Aspects of the Hyperimmune-Free Degrees (K M Ng, F Stephan, Y Yang and L Yu)Calibrating the Complexity of Δ02 Sets via Their Changes (A Nies)Topological Full Groups of Minimal Subshifts and Just-Infnite Groups (S Thomas)TW-Models for Logic of Knowledge-cum-Belief (S C-M Yang) Readership: Researchers in mathematical logic and algebra, computer scientists in artificial intelligence and fuzzy logic. Keywords:Asian Logic Conference;Logic;Computability;Set Theory;Modal Logic
Book Synopsis Models, Modules and Abelian Groups by : Rüdiger Göbel
Download or read book Models, Modules and Abelian Groups written by Rüdiger Göbel and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a memorial volume dedicated to A. L. S. Corner, previously Professor in Oxford, who published important results on algebra, especially on the connections of modules with endomorphism algebras. The volume contains refereed contributions which are related to the work of Corner. It contains also an unpublished extended paper of Corner himself. A memorial volume with important contributions related to algebra.
Download or read book Advances in Logic written by Su Gao and published by American Mathematical Soc.. This book was released on 2007 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book are based on talks given at the North Texas Logic Conference in October of 2004. The main goal of the editors was to collect articles representing diverse fields within logic that would both contain significant new results and be accessible to readers with a general background in logic. Included in the book is a problem list, jointly compiled by the speakers, that reflects some of the most important questions in various areas of logic. This book should be useful to graduate students and researchers alike across the spectrum of mathematical logic.
Book Synopsis Proceedings of the 12th Asian Logic Conference, Wellington, New Zealand, 15-20 December 2011 by : Rod G. Downey
Download or read book Proceedings of the 12th Asian Logic Conference, Wellington, New Zealand, 15-20 December 2011 written by Rod G. Downey and published by World Scientific. This book was released on 2013 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Asian Logic Conference is one of the largest meetings, and this volume represents work presented at, and arising from the 12th meeting. It collects a number of interesting papers from experts in the field. It covers many areas of logic.
Book Synopsis Effective Mathematics of the Uncountable by : Noam Greenberg
Download or read book Effective Mathematics of the Uncountable written by Noam Greenberg and published by Cambridge University Press. This book was released on 2013-10-31 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical computable model theory is most naturally concerned with countable domains. There are, however, several methods – some old, some new – that have extended its basic concepts to uncountable structures. Unlike in the classical case, however, no single dominant approach has emerged, and different methods reveal different aspects of the computable content of uncountable mathematics. This book contains introductions to eight major approaches to computable uncountable mathematics: descriptive set theory; infinite time Turing machines; Blum-Shub-Smale computability; Sigma-definability; computability theory on admissible ordinals; E-recursion theory; local computability; and uncountable reverse mathematics. This book provides an authoritative and multifaceted introduction to this exciting new area of research that is still in its early stages. It is ideal as both an introductory text for graduate and advanced undergraduate students and a source of interesting new approaches for researchers in computability theory and related areas.
