Canonical Ramsey theory on Polish spaces
 Author/Creator
 Kanoveĭ, V. G. (Vladimir Grigorʹevich)
 Language
 English.
 Imprint
 Cambridge : Cambridge University Press, 2013.
 Physical description
 viii, 269 p. ; 24 cm.
 Series
 Cambridge tracts in mathematics ; 202.
Access
Available online

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QA248 .K356 2013

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QA248 .K356 2013
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Contributors
 Contributor
 Sabok, Marcin.
 Zapletal, Jindřich, 1969
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 264267) and index.
 Contents

 Preface 1. Introduction 2. Background facts 3. Analytic equivalence relations and models of set theory 4. Classes of equivalence relations 5. Games and the Silver property 6. The game ideals 7. Benchmark equivalence relations 8. Ramseytype ideals 9. Producttype ideals 10. The countable support iteration ideals References Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and GandyHarrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigmaideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal.
 Series
 Cambridge tracts in mathematics ; 202
 ISBN
 9781107026858
 1107026857