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Canonical Ramsey theory on Polish spaces

Kanovei, V. G.

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Canonical Ramsey theory on Polish spaces

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Canonical Ramsey theory on Polish spaces/ Vladimir Kanovei, Marcin Sabok, Jindrich Zapletal.
作者:	Kanovei, V. G.
其他作者:	Sabok, Marcin.
出版者:	Cambridge :Cambridge University Press, : 2013.,
面頁冊數:	viii, 269 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	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.
標題:	Set theory. -
電子資源:	https://doi.org/10.1017/CBO9781139208666
ISBN:	9781139208666

Canonical Ramsey theory on Polish spaces
Kanovei, V. G.

Canonical Ramsey theory on Polish spaces[electronic resource] /Vladimir Kanovei, Marcin Sabok, Jindrich Zapletal. - Cambridge :Cambridge University Press,2013. - viii, 269 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;202. - Cambridge tracts in mathematics ;202..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

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: 9781139208666Subjects--Topical Terms:

520081
Set theory.

LC Class. No.: QA248 / .K356 2013

Dewey Class. No.: 511.322

Canonical Ramsey theory on Polish spaces
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
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