Canonical Ramsey theory on Polish spaces / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal.

Format:

Book

Author/Creator:

Kanoveĭ, V. G. (Vladimir Grigorʹevich), author.

Sabok, Marcin, author.

Zapletal, Jindřich, 1969- author.

Series:

Cambridge tracts in mathematics ; 202.

Cambridge tracts in mathematics ; 202

Language:

English

Subjects (All):

Set theory.

Ramsey theory.

Polish spaces (Mathematics).

Physical Description:

1 online resource (viii, 269 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2013.

Language Note:

English

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.

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-42423-2

1-139-89113-8

1-107-42195-0

1-107-41924-7

1-107-41660-4

1-139-20866-7

1-107-42047-4

1-107-41792-9

OCLC:

863821791