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Canonical Ramsey Theory on Polish Spaces, EPUB eBook

Canonical Ramsey Theory on Polish Spaces EPUB

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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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