Canonical Ramsey theory on Polish spaces /
Kanoveĭ, V. G.
Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. - Cambridge : Cambridge University Press, 2013. - 1 online resource (viii, 269 pages) : digital, PDF file(s). - 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.
9781139208666 (ebook)
Set theory.
Ramsey theory.
Polish spaces (Mathematics)
QA248 / .K356 2013
511.322
Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. - Cambridge : Cambridge University Press, 2013. - 1 online resource (viii, 269 pages) : digital, PDF file(s). - 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.
9781139208666 (ebook)
Set theory.
Ramsey theory.
Polish spaces (Mathematics)
QA248 / .K356 2013
511.322