Canonical Ramsey theory on polish spaces
Author(s)
Bibliographic Information
Canonical Ramsey theory on polish spaces
（Cambridge tracts in mathematics, 202）
Cambridge University Press, 2013
- : hardback
Available at / 27 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackKAN||17||3200026147922
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: hardback/K 1332080336920
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Note
Includes bibliographical references (p. 264-267) and index
Description and Table of Contents
Description
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 Gandy-Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, 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.
Table of 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. Ramsey-type ideals
- 9. Product-type ideals
- 10. The countable support iteration ideals
- References
- Index.
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