| Description |
1 online resource (viii, 269 pages) |
| Series |
Cambridge tracts in mathematics ; 202 |
|
Cambridge tracts in mathematics ; 202
|
| 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 -- Ramsey-type ideals -- Product-type 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 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 |
| Bibliography |
Includes bibliographical references (pages 264-267) and index |
| Notes |
Print version record |
| Subject |
Set theory.
|
|
Ramsey theory.
|
|
Polish spaces (Mathematics)
|
|
MATHEMATICS -- General.
|
|
Polish spaces (Mathematics)
|
|
Ramsey theory.
|
|
Set theory.
|
| Form |
Electronic book
|
| Author |
Sabok, Marcin
|
|
Zapletal, Jindřich, 1969-
|
| ISBN |
9781107416604 |
|
1107416604 |
|
9781139208666 |
|
1139208667 |
|
9781306071963 |
|
1306071968 |
|
9781107419247 |
|
1107419247 |
|
9781107420472 |
|
1107420474 |
|
