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Author Kanoveĭ, V. G. (Vladimir Grigorʹevich)

Title Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal
Published Cambridge : Cambridge University Press, 2013


Description 1 online resource (viii, 269 pages)
Series Cambridge tracts in mathematics ; 202
Cambridge tracts in mathematics ; 202
Contents Introduction -- Background facts -- Analytic equivalence relations and models of set theory -- Classes of equivalence relations -- Games and the Silver property -- The game ideals -- Benchmark equivalence relations -- Ramsey-type ideals -- Product-type ideals -- The countable support iteration ideals
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
Bibliography Includes bibliographical references (pages 264-267) and index
Notes Print version record
Subject Set theory.
Ramsey theory.
Polish spaces (Mathematics)
Polish spaces (Mathematics)
Ramsey theory.
Set theory.
Form Electronic book
Author Sabok, Marcin
Zapletal, Jindřich, 1969-
ISBN 9781107416604