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Author Kanoveĭ, V. G. (Vladimir Grigorʹevich)
Title Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindrich 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.
Note Print version record.
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.
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: Kanovei, V.G. (Vladimir Grigorevich). Canonical Ramsey theory on Polish spaces 9781107026858 (OCoLC)847601579.