Kechris, A. S. 1946
Overview
Works:  87 works in 342 publications in 3 languages and 7,047 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Thesis advisor, edc 
Classifications:  QA3, 511.322 
Publication Timeline
.
Most widely held works by
A. S Kechris
Descriptive set theory and the structure of sets of uniqueness by
A. S Kechris(
)
21 editions published between 1987 and 2005 in English and held by 1,182 WorldCat member libraries worldwide
The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the midnineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially selfcontained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis
21 editions published between 1987 and 2005 in English and held by 1,182 WorldCat member libraries worldwide
The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the midnineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially selfcontained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis
The descriptive set theory of Polish group actions by
Howard Paul Becker(
)
14 editions published in 1996 in English and held by 1,105 WorldCat member libraries worldwide
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. Nonlocally 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, GlimmEffros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces
14 editions published in 1996 in English and held by 1,105 WorldCat member libraries worldwide
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. Nonlocally 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, GlimmEffros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces
Cabal Seminar 7677 : proceedings, CaltechUCLA logic seminar 197677 by
A. S Kechris(
Book
)
24 editions published between 1978 and 2006 in English and Undetermined and held by 526 WorldCat member libraries worldwide
24 editions published between 1978 and 2006 in English and Undetermined and held by 526 WorldCat member libraries worldwide
Cabal seminar 7779 : proceedings, CaltechUCLA logic seminar 197779 by
Cabal Seminar(
Book
)
23 editions published between 1981 and 2006 in English and Undetermined and held by 516 WorldCat member libraries worldwide
23 editions published between 1981 and 2006 in English and Undetermined and held by 516 WorldCat member libraries worldwide
Classical descriptive set theory by
A. S Kechris(
Book
)
19 editions published between 1994 and 2012 in English and Hungarian and held by 515 WorldCat member libraries worldwide
Descriptive set theory is the area of mathematics concerned with the study of the structure of definable sets in Polish spaces. Beyond being a central part of contemporary set theory, the concepts and results of descriptive set theory are being used in diverse fields of mathematics, such as logic, combinatorics, topology, Banach space theory, real and harmonic analysis, potential theory, ergodic theory, operator algebras, and group representation theory. This book provides a basic first introduction to the subject at the beginning graduate level. It concentrates on the core classical aspects, but from a modern viewpoint, including many recent developments, like games and determinacy, and illustrates the general theory by numerous examples and applications to other areas of mathematics. The book, which is written in the style of informal lecture notes, consists of five chapters. The first contains the basic theory of Polish spaces and its standard tools, like Baire category. The second deals with the theory of Borel sets. Methods of infinite games figure prominently here as well as in subsequent chapters. The third chapter is devoted to the analytic sets and the fourth to the coanalytic sets, developing the machinery associated with ranks and scales. The final chapter gives an introduction to the projective sets, including the periodicity theorems. The book contains over four hundred exercises of varying degrees of difficulty
19 editions published between 1994 and 2012 in English and Hungarian and held by 515 WorldCat member libraries worldwide
Descriptive set theory is the area of mathematics concerned with the study of the structure of definable sets in Polish spaces. Beyond being a central part of contemporary set theory, the concepts and results of descriptive set theory are being used in diverse fields of mathematics, such as logic, combinatorics, topology, Banach space theory, real and harmonic analysis, potential theory, ergodic theory, operator algebras, and group representation theory. This book provides a basic first introduction to the subject at the beginning graduate level. It concentrates on the core classical aspects, but from a modern viewpoint, including many recent developments, like games and determinacy, and illustrates the general theory by numerous examples and applications to other areas of mathematics. The book, which is written in the style of informal lecture notes, consists of five chapters. The first contains the basic theory of Polish spaces and its standard tools, like Baire category. The second deals with the theory of Borel sets. Methods of infinite games figure prominently here as well as in subsequent chapters. The third chapter is devoted to the analytic sets and the fourth to the coanalytic sets, developing the machinery associated with ranks and scales. The final chapter gives an introduction to the projective sets, including the periodicity theorems. The book contains over four hundred exercises of varying degrees of difficulty
Topics in orbit equivalence by
A. S Kechris(
Book
)
17 editions published in 2004 in English and held by 496 WorldCat member libraries worldwide
"This volume provides a selfcontained 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 measurepreserving, ergodic actions of the integers are orbit equivalent and of the theorem of ConnesFeldmanWeiss identifying amenability and hyperfiniteness for nonsingular 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."Résumé de l'éditeur
17 editions published in 2004 in English and held by 496 WorldCat member libraries worldwide
"This volume provides a selfcontained 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 measurepreserving, ergodic actions of the integers are orbit equivalent and of the theorem of ConnesFeldmanWeiss identifying amenability and hyperfiniteness for nonsingular 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."Résumé de l'éditeur
Cabal Seminar 8185 : proceedings, CaltechUCLA Logic Seminar, 198185 by
Los Angeles, Calif.) Cabal Seminar (1981  1985(
Book
)
21 editions published in 1988 in 3 languages and held by 475 WorldCat member libraries worldwide
This is the fourth volume of the proceeding of the CaltechUCLA Logic Seminar, based mainly on material which was presented and discussed in the period 198185, but containing also some very recent results. It includes research papers dealing with determinacy hypotheses and their consequences in descriptive set theory. An appendix contains the new Victoria Delfino Problems
21 editions published in 1988 in 3 languages and held by 475 WorldCat member libraries worldwide
This is the fourth volume of the proceeding of the CaltechUCLA Logic Seminar, based mainly on material which was presented and discussed in the period 198185, but containing also some very recent results. It includes research papers dealing with determinacy hypotheses and their consequences in descriptive set theory. An appendix contains the new Victoria Delfino Problems
Cabal Seminar 7981 : proceedings, CaltechUCLA Logic Seminar 197981 by
Cabal Seminar(
Book
)
18 editions published between 1978 and 1983 in English and Undetermined and held by 467 WorldCat member libraries worldwide
18 editions published between 1978 and 1983 in English and Undetermined and held by 467 WorldCat member libraries worldwide
Global aspects of ergodic group actions by
A. S Kechris(
Book
)
12 editions published in 2010 in English and held by 292 WorldCat member libraries worldwide
"The subject of this book is the study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces. These are equipped with canonical topological actions that give rise to the usual concepts of conjugacy of actions and cohomology of cocycles. Structural properties of discrete groups such as amenability, Kazhdan's property (T) and the Haagerup Approximation Property play a significant role in this theory as they have important connections to the global structure of these spaces. One of the main topics discussed in this book is the analysis of the complexity of the classification problems of conjugacy and orbit equivalence of actions, as well as of cohomology of cocycles. This involves ideas from topological dynamics, descriptive set theory, harmonic analysis, and the theory of unitary group representations. Also included is a study of properties of the automorphism group of a standard probability space and some of its important subgroups, such as the full and automorphism groups of measure preserving equivalence relations and connections with the theory of costs. The book contains nine appendices that present necessary background material in functional analysis, measure theory, and group representations, thus making the book accessible to a wider audience."Publisher's website
12 editions published in 2010 in English and held by 292 WorldCat member libraries worldwide
"The subject of this book is the study of ergodic, measure preserving actions of countable discrete groups on standard probability spaces. It explores a direction that emphasizes a global point of view, concentrating on the structure of the space of measure preserving actions of a given group and its associated cocycle spaces. These are equipped with canonical topological actions that give rise to the usual concepts of conjugacy of actions and cohomology of cocycles. Structural properties of discrete groups such as amenability, Kazhdan's property (T) and the Haagerup Approximation Property play a significant role in this theory as they have important connections to the global structure of these spaces. One of the main topics discussed in this book is the analysis of the complexity of the classification problems of conjugacy and orbit equivalence of actions, as well as of cohomology of cocycles. This involves ideas from topological dynamics, descriptive set theory, harmonic analysis, and the theory of unitary group representations. Also included is a study of properties of the automorphism group of a standard probability space and some of its important subgroups, such as the full and automorphism groups of measure preserving equivalence relations and connections with the theory of costs. The book contains nine appendices that present necessary background material in functional analysis, measure theory, and group representations, thus making the book accessible to a wider audience."Publisher's website
Rigidity theorems for actions of product groups and countable Borel equivalence relations by
Greg Hjorth(
Book
)
10 editions published in 2005 in English and Undetermined and held by 255 WorldCat member libraries worldwide
Introduction Preliminaries Actions of free groups and treeable equivalence relations A cocycle reduction result Some applications Factoring homomorphisms Further applications Product actions, I Product actions, II A Final application Appendix A. Strong notions of ergodicity Appendix B. Cocycles and cocycleinvariant functions Appendix C. Actions on boundaries Appendix D. $\mathcal{K}$structured Equivalence relations Appendix E. Proof of the general case of Theorem 4.4 Bibliography
10 editions published in 2005 in English and Undetermined and held by 255 WorldCat member libraries worldwide
Introduction Preliminaries Actions of free groups and treeable equivalence relations A cocycle reduction result Some applications Factoring homomorphisms Further applications Product actions, I Product actions, II A Final application Appendix A. Strong notions of ergodicity Appendix B. Cocycles and cocycleinvariant functions Appendix C. Actions on boundaries Appendix D. $\mathcal{K}$structured Equivalence relations Appendix E. Proof of the general case of Theorem 4.4 Bibliography
On the classification of Polish metric spaces up to isometry by
Su Gao(
Book
)
9 editions published in 2003 in English and held by 253 WorldCat member libraries worldwide
9 editions published in 2003 in English and held by 253 WorldCat member libraries worldwide
The Cabal Seminar(
Book
)
7 editions published in 2008 in English and held by 132 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Games and Scales' (Part 1) and 'Suslin Cardinals, Partition Properties, and Homogeneity' (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context. This volume will be an invaluable reference for anyone interested in higher set theory
7 editions published in 2008 in English and held by 132 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Games and Scales' (Part 1) and 'Suslin Cardinals, Partition Properties, and Homogeneity' (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context. This volume will be an invaluable reference for anyone interested in higher set theory
Ordinal Definability and Recursion Theory by
A. S Kechris(
)
10 editions published between 2015 and 2016 in English and held by 81 WorldCat member libraries worldwide
The third in a series of four books presenting the seminal papers from the CaltechUCLA 'Cabal Seminar'
10 editions published between 2015 and 2016 in English and held by 81 WorldCat member libraries worldwide
The third in a series of four books presenting the seminal papers from the CaltechUCLA 'Cabal Seminar'
The Cabal Seminar(
)
5 editions published between 2011 and 2012 in English and held by 81 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist
5 editions published between 2011 and 2012 in English and held by 81 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist
Wadge degrees and projective ordinals : the Cabal Seminar by
A. S Kechris(
)
11 editions published between 2011 and 2012 in English and held by 70 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist
11 editions published between 2011 and 2012 in English and held by 70 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist
Cabal Seminar 77  79 : Proceedings, CaltechUCLA Logic Seminar 1977  79 by CaltechUCLA Logic Seminar(
)
2 editions published in 1981 in English and held by 67 WorldCat member libraries worldwide
2 editions published in 1981 in English and held by 67 WorldCat member libraries worldwide
The Cabal seminar by
A. S Kechris(
)
6 editions published between 2015 and 2016 in English and Undetermined and held by 61 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist
6 editions published between 2015 and 2016 in English and Undetermined and held by 61 WorldCat member libraries worldwide
The proceedings of the Los Angeles CaltechUCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist
Cabal Seminar 7677 : Proceedings, CaltechUCLA Logic Seminar 197677(
)
1 edition published in 1978 in English and held by 39 WorldCat member libraries worldwide
1 edition published in 1978 in English and held by 39 WorldCat member libraries worldwide
Cabal seminar 7981 : proceedings of the CaltechUCLA logic seminar in 19791981 by
A. S Kechris(
)
9 editions published between 1981 and 1983 in English and Undetermined and held by 39 WorldCat member libraries worldwide
9 editions published between 1981 and 1983 in English and Undetermined and held by 39 WorldCat member libraries worldwide
Cabal Seminar 7981 : Proceedings, CaltechUCLA Logic Seminar 197981(
)
1 edition published in 1983 in English and held by 38 WorldCat member libraries worldwide
1 edition published in 1983 in English and held by 38 WorldCat member libraries worldwide
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Related Identities
 Moschovakis, Yiannis N. Other Author Editor
 Martin, D. A. (Donald A.) 1940 Other Author Editor
 Louveau, Alain Other
 Becker, Howard Author
 Steel, J. R. (John R.) 1948 Other Author Editor
 Löwe, Benedikt Editor
 Gao, Su 1968 Author
 Hjorth, Greg 1963 Author
 Miller, Benjamin David 1977
 California Institute of Technology (Pasadena, Calif.) Other
Useful Links
Associated Subjects
Automorphisms Borel sets Descriptive set theory Differentiable dynamical systems Equivalence classes (Set theory) Equivalence relations (Set theory) Ergodic theory Fourier series Game theory Harmonic analysis Logic, Symbolic and mathematical Mathematics Measurepreserving transformations Measure theory Polish spaces (Mathematics) Recursion theory Rigidity (Geometry) Set theory Topological transformation groups Topology
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Alternative Names
Alexander S. Kechris Amerikaans wiskundige
Alexander S. Kechris amerikansk matematikar
Alexander S. Kechris amerikansk matematiker
Alexander S. Kechris matematico statunitense
Alexander S. Kechris USamerikanischer Logiker
Alexander Sotirios Kechris
Kechris, A.
Kechris, A.S.
Kechris, A. S. 1946
Kechris, Alexander 1946
Kechris, Alexander S.
Kechris, Alexander S. 1946
Kechris, Alexander Sotirios.
Kechris, Alexander Sotirios 1946
アレキサンダー・ケクリス
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