Canonical Ramsey Theory on Polish Spaces

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Canonical Ramsey Theory on Polish Spaces

Vladimir Kanovei, "Canonical Ramsey Theory on Polish Spaces"
English | ISBN: 1107026857 | 2013 | 278 pages | PDF | 2 MB

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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Tags: Canonical, Ramsey, Theory, Polish, Spaces

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