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  1. Home
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  3. Canonical Ramsey Theory on Polish Spaces
  • Cited by 17
Publisher:
Cambridge University Press
Online publication date:
December 2013
Print publication year:
2013
Online ISBN:
9781139208666
DOI:
https://doi.org/10.1017/CBO9781139208666
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets
Series:
Cambridge Tracts in Mathematics (202)
Information

Book description

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.

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Contents

Contents
References
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