Series 
Cambridge tracts in mathematics ; 202 

Cambridge tracts in mathematics ;
202.

Subject 
Set theory.


Ramsey theory.


Polish spaces (Mathematics)

Alt Name 
Sabok, Marcin.


Zapletal, Jindřich, 1969

Description 
1 online resource (viii, 269 pages). 
Bibliography Note 
Includes bibliographical references (pages 264267) and index. 
Contents 
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  Ramseytype ideals  Producttype ideals  The countable support iteration ideals. 
Summary 
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 sigmaideals, 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. 
Note 
Print version record. 
ISBN 
9781107416604 (electronic bk.) 

1107416604 (electronic bk.) 

9781139208666 (electronic bk.) 

1139208667 (electronic bk.) 

9781306071963 (MyiLibrary) 

1306071968 (MyiLibrary) 

9781107419247 

1107419247 

9781107420472 (ebook) 

1107420474 (ebook) 

9781107026858 

1107026857 
OCLC # 
861693020 
Additional Format 
Print version: Kanoveĭ, V.G. (Vladimir Grigorʹevich). Canonical Ramsey theory on Polish spaces 9781107026858 (OCoLC)847601579 
