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Author Kanoveĭ, V. G. (Vladimir Grigorʹevich)
Title Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal.
Imprint Cambridge : Cambridge University Press, 2013.

Series Cambridge tracts in mathematics ; 202
Cambridge tracts in mathematics ; 202.
Subject Set theory.
Ramsey theory.
Polish spaces (Mathematics)
Alt Name Sabok, Marcin.
Zapletal, Jindřich, 1969-
Description 1 online resource (viii, 269 pages).
Bibliography Note Includes bibliographical references (pages 264-267) and index.
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.
Note Print version record.
ISBN 9781107416604 (electronic bk.)
1107416604 (electronic bk.)
9781139208666 (electronic bk.)
1139208667 (electronic bk.)
9781306071963 (MyiLibrary)
1306071968 (MyiLibrary)
9781107420472 (e-book)
1107420474 (e-book)
OCLC # 861693020
Additional Format Print version: Kanoveĭ, V.G. (Vladimir Grigorʹevich). Canonical Ramsey theory on Polish spaces 9781107026858 (OCoLC)847601579