Canonical Ramsey theory on Polish spaces
- Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal.
- Cambridge : Cambridge University Press, 2013.
- Physical description
- viii, 269 p. ; 24 cm.
- Cambridge tracts in mathematics ; 202.
Math & Statistics Library
QA248 .K356 2013
- Unknown QA248 .K356 2013
- Includes bibliographical references (p. 264-267) and index.
- 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.
- (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 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.
(source: Nielsen Book Data)
- Publication date
- Cambridge tracts in mathematics ; 202
- 9781107026858 (hbk.)
- 1107026857 (hbk.)