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Canonical Ramsey Theory on Polish Spaces
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SYSNO ASEP 0422163 Document Type B - Monograph R&D Document Type Monograph Title Canonical Ramsey Theory on Polish Spaces Author(s) Kanovei, V. (RU)
Sabok, M. (PL)
Zapletal, Jindřich (MU-W) RID, SAI, ORCIDIssue data Cambridge: Cambridge University Press, 2013 ISBN 978-1-107-02685-8 Series Cambridge Tracts in Mathematics Series number 202 Number of pages 269 s. Number of copy 500 Publication form Print - P Language eng - English Country GB - United Kingdom Issue 1. Keywords Borel equivalence-relations ; sigma-porous sets ; closed-sets Subject RIV BA - General Mathematics R&D Projects MEB051006 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) MEB060909 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) IAA100190902 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) Institutional support MU-W - RVO:67985840 CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000325694000012 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2014
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