Canonical Ramsey Theory on Polish Spaces
$142.00 (C)
Part of Cambridge Tracts in Mathematics
- Authors:
- Vladimir Kanovei, Russian Academy of Sciences, Moscow
- Marcin Sabok, Polish Academy of Sciences
- Jindřich Zapletal, University of Florida
- Date Published: October 2013
- availability: Available
- format: Hardback
- isbn: 9781107026858
$
142.00
(C)
Hardback
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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.
Read more- Explores a new line of research in set theory
- Contains previously unpublished results
- Opens up avenues for further investigation
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×Product details
- Date Published: October 2013
- format: Hardback
- isbn: 9781107026858
- length: 278 pages
- dimensions: 235 x 157 x 19 mm
- weight: 0.53kg
- availability: Available
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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