03470nam 22007212 450 991082363670332120151005020622.01-107-42423-21-139-89113-81-107-42195-01-107-41924-71-107-41660-41-139-20866-71-107-42047-41-107-41792-9(CKB)2550000001138777(EBL)1394548(OCoLC)863821791(SSID)ssj0001058917(PQKBManifestationID)12458504(PQKBTitleCode)TC0001058917(PQKBWorkID)11070788(PQKB)11165079(UkCbUP)CR9781139208666(Au-PeEL)EBL1394548(CaPaEBR)ebr10774116(CaONFJC)MIL538447(MiAaPQ)EBC1394548(PPN)26129587X(EXLCZ)99255000000113877720111208d2013|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierCanonical Ramsey theory on Polish spaces /Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal[electronic resource]Cambridge :Cambridge University Press,2013.1 online resource (viii, 269 pages) digital, PDF file(s)Cambridge tracts in mathematics ;202Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-02685-7 1-306-07196-8 Includes bibliographical references and index.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.Cambridge tracts in mathematics ;202.Set theoryRamsey theoryPolish spaces (Mathematics)Set theory.Ramsey theory.Polish spaces (Mathematics)511.322Kanoveĭ V. G(Vladimir Grigorʹevich),504970Sabok MarcinZapletal Jindřich1969-UkCbUPUkCbUPBOOK9910823636703321Canonical Ramsey theory on Polish spaces4029850UNINA