1.

Record Nr.

UNINA9910823636703321

Autore

Kanoveĭ V. G (Vladimir Grigorʹevich)

Titolo

Canonical Ramsey theory on Polish spaces / / Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal [[electronic resource]]

Pubbl/distr/stampa

Cambridge : , : Cambridge University Press, , 2013

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

Descrizione fisica

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

Collana

Cambridge tracts in mathematics ; ; 202

Disciplina

511.322

Soggetti

Set theory

Ramsey theory

Polish spaces (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

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

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.