Canonical Ramsey theory on Polish spaces / / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal [[electronic resource]]

• Autore: Kanoveĭ V. G (Vladimir Grigorʹevich)
• Pubblicazione: Cambridge : , : Cambridge University Press, , 2013
• Descrizione fisica: 1 online resource (viii, 269 pages) : digital, PDF file(s)
• Disciplina: 511.322
• Soggetto topico: Set theory; Ramsey theory; Polish spaces (Mathematics)
• Persona (resp. second.): SabokMarcin; ZapletalJindřich <1969->
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Canonical Ramsey theory on Polish spaces
• ISBN: 1-107-42423-2; 1-139-89113-8; 1-107-42195-0; 1-107-41924-7; 1-107-41660-4; 1-139-20866-7; 1-107-42047-4; 1-107-41792-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910453378703321
• Lo trovi qui: Univ. Federico II
• Serie: Cambridge tracts in mathematics ; ; 202.