TY  - BOOK
AU  - Kanoveĭ,V.G.
AU  - Sabok,Marcin
AU  - Zapletal,Jindřich
TI  - Canonical Ramsey theory on Polish spaces
T2  - Cambridge tracts in mathematics
SN  - 9781139208666 (ebook)
AV  - QA248 .K356 2013
U1  - 511.322 23
PY  - 2013///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Set theory
KW  - Ramsey theory
KW  - Polish spaces (Mathematics)
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); 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
N2  - 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
UR  - https://doi.org/10.1017/CBO9781139208666
ER  -