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200 10$aCanonical Ramsey theory on Polish spaces /$fVladimir Kanovei, Marcin Sabok, Jindr?ich Zapletal$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2013.
215   $a1 online resource (viii, 269 pages) $cdigital, PDF file(s)
225 1 $aCambridge tracts in mathematics ;$v202
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a1-107-02685-7 
311   $a1-306-07196-8 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- 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.
330   $aThis book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy-Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.
410  0$aCambridge tracts in mathematics ;$v202.
606   $aSet theory
606   $aRamsey theory
606   $aPolish spaces (Mathematics)
615  0$aSet theory.
615  0$aRamsey theory.
615  0$aPolish spaces (Mathematics)
676   $a511.322
700   $aKanovei?$b V. G$g(Vladimir Grigor?evich),$0504970
702   $aSabok$b Marcin
702   $aZapletal$b Jindr?ich$f1969-
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910823636703321
996   $aCanonical Ramsey theory on Polish spaces$94029850
997   $aUNINA