Kanoveĭ, V. G. <br/><br/>
Canonical Ramsey theory on Polish spaces / 
Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal. 
 - Cambridge :  Cambridge University Press,  2013. 
 - 1 online resource (viii, 269 pages) :  digital, PDF file(s). 
 - Cambridge tracts in mathematics ;  202 .
 - Cambridge tracts in mathematics ;  202. .
<br/><br/> Title from publisher's bibliographic system (viewed on 05 Oct 2015). 
<br/><br/>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. 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9781139208666 (ebook) 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Set theory.<br/>Ramsey theory.<br/>Polish spaces (Mathematics)
<br/><br/><label>LC Class. No.: </label>QA248  / .K356 2013 
<br/><br/><label>Dewey Class. No.: </label>511.322