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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.
  • ISBN13: 9781107026858
  • Publisher: Cambridge University Press
  • Pubilcation Year: 2013
  • Format: Hardcover
  • Pages: 00278
Specifications
FormatHardcover
SeriesCambridge Tracts in Mathematics (Hardcover)
Series Volume Number202
Publication DateSeptember 12, 2013

Canonical Ramsey Theory on Polish Spaces

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