Canonical Ramsey theory on Polish spaces /:
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 analy...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2013.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
202. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (viii, 269 pages) |
| Bibliographie: | Includes bibliographical references (pages 264-267) and index. |
| ISBN: | 9781107416604 1107416604 9781139208666 1139208667 9781306071963 1306071968 9781107419247 1107419247 9781107420472 1107420474 |
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| 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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| author | Kanoveĭ, V. G. (Vladimir Grigorʹevich) |
| author2 | Sabok, Marcin Zapletal, Jindřich, 1969- |
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| contents | 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. |
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| series2 | Cambridge tracts in mathematics ; |
| spelling | Kanoveĭ, V. G. (Vladimir Grigorʹevich) http://id.loc.gov/authorities/names/n85358241 Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. Cambridge : Cambridge University Press, 2013. 1 online resource (viii, 269 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 202 Includes bibliographical references (pages 264-267) and index. Print version record. 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. Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Ramsey theory. http://id.loc.gov/authorities/subjects/sh85111302 Polish spaces (Mathematics) http://id.loc.gov/authorities/subjects/sh91000874 Théorie des ensembles. Théorie de Ramsey. Espaces polonais (Mathématiques) MATHEMATICS General. bisacsh Teoría de juegos embne Polish spaces (Mathematics) fast Ramsey theory fast Set theory fast Electronic book. Sabok, Marcin. Zapletal, Jindřich, 1969- http://id.loc.gov/authorities/names/n2003013917 Print version: Kanoveĭ, V.G. (Vladimir Grigorʹevich). Canonical Ramsey theory on Polish spaces 9781107026858 (OCoLC)847601579 Cambridge tracts in mathematics ; 202. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=622090 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=622090 Volltext |
| spellingShingle | Kanoveĭ, V. G. (Vladimir Grigorʹevich) Canonical Ramsey theory on Polish spaces / Cambridge tracts in mathematics ; 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. Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Ramsey theory. http://id.loc.gov/authorities/subjects/sh85111302 Polish spaces (Mathematics) http://id.loc.gov/authorities/subjects/sh91000874 Théorie des ensembles. Théorie de Ramsey. Espaces polonais (Mathématiques) MATHEMATICS General. bisacsh Teoría de juegos embne Polish spaces (Mathematics) fast Ramsey theory fast Set theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85120387 http://id.loc.gov/authorities/subjects/sh85111302 http://id.loc.gov/authorities/subjects/sh91000874 |
| title | Canonical Ramsey theory on Polish spaces / |
| title_auth | Canonical Ramsey theory on Polish spaces / |
| title_exact_search | Canonical Ramsey theory on Polish spaces / |
| title_full | Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. |
| title_fullStr | Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. |
| title_full_unstemmed | Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. |
| title_short | Canonical Ramsey theory on Polish spaces / |
| title_sort | canonical ramsey theory on polish spaces |
| topic | Set theory. http://id.loc.gov/authorities/subjects/sh85120387 Ramsey theory. http://id.loc.gov/authorities/subjects/sh85111302 Polish spaces (Mathematics) http://id.loc.gov/authorities/subjects/sh91000874 Théorie des ensembles. Théorie de Ramsey. Espaces polonais (Mathématiques) MATHEMATICS General. bisacsh Teoría de juegos embne Polish spaces (Mathematics) fast Ramsey theory fast Set theory fast |
| topic_facet | Set theory. Ramsey theory. Polish spaces (Mathematics) Théorie des ensembles. Théorie de Ramsey. Espaces polonais (Mathématiques) MATHEMATICS General. Teoría de juegos Ramsey theory Set theory Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=622090 |
| work_keys_str_mv | AT kanoveivg canonicalramseytheoryonpolishspaces AT sabokmarcin canonicalramseytheoryonpolishspaces AT zapletaljindrich canonicalramseytheoryonpolishspaces |