Canonical Ramsey theory on Polish spaces /
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| Author / Creator: | Kanoveĭ, V. G. (Vladimir Grigorʹevich) |
|---|---|
| Imprint: | Cambridge : Cambridge University Press, 2013. |
| Description: | 1 online resource (viii, 269 pages) |
| Language: | English |
| Series: | Cambridge tracts in mathematics ; 202 Cambridge tracts in mathematics ; 202. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11831896 |
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| 100 | 1 | |a Kanoveĭ, V. G. |q (Vladimir Grigorʹevich) |0 http://id.loc.gov/authorities/names/n85358241 | |
| 245 | 1 | 0 | |a Canonical Ramsey theory on Polish spaces / |c Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2013. | |
| 300 | |a 1 online resource (viii, 269 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics ; |v 202 | |
| 504 | |a Includes bibliographical references (pages 264-267) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 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. | ||
| 650 | 0 | |a Set theory. |0 http://id.loc.gov/authorities/subjects/sh85120387 | |
| 650 | 0 | |a Ramsey theory. |0 http://id.loc.gov/authorities/subjects/sh85111302 | |
| 650 | 0 | |a Polish spaces (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh91000874 | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Polish spaces (Mathematics) |2 fast |0 (OCoLC)fst01069157 | |
| 650 | 7 | |a Ramsey theory. |2 fast |0 (OCoLC)fst01089712 | |
| 650 | 7 | |a Set theory. |2 fast |0 (OCoLC)fst01113587 | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Sabok, Marcin. | |
| 700 | 1 | |a Zapletal, Jindřich, |d 1969- |0 http://id.loc.gov/authorities/names/n2003013917 | |
| 776 | 0 | 8 | |i Print version: |a Kanoveĭ, V.G. (Vladimir Grigorʹevich). |t Canonical Ramsey theory on Polish spaces |z 9781107026858 |w (OCoLC)847601579 |
| 830 | 0 | |a Cambridge tracts in mathematics ; |v 202. |0 http://id.loc.gov/authorities/names/n42005726 | |
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| 928 | |t Library of Congress classification |a QA248 .K356 2013eb |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=622090 |z eBooks on EBSCOhost |g ebooks |i 12398129 | ||