Canonical Ramsey Theory on Polish Spaces

0422163 - MÚ 2014 RIV GB eng B - Monography
Kanovei, V. - Sabok, M. - Zapletal, Jindřich
Canonical Ramsey Theory on Polish Spaces.
1. - Cambridge: Cambridge University Press, 2013. 269 s. Cambridge Tracts in Mathematics, 202. ISBN 978-1-107-02685-8
R&D Projects: GA MŠMT MEB051006; GA MŠMT MEB060909; GA AV ČR IAA100190902
Institutional research plan: CEZ:AV0Z10190503
Institutional support: RVO:67985840
Keywords : Borel equivalence-relations * sigma-porous sets * closed-sets
Subject RIV: BA - General Mathematics

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.
Permanent Link: http://hdl.handle.net/11104/0228363