Canonical Ramsey Theory on Polish Spaces (Cambridge Tracts by Vladimir Kanovei,Marcin Sabok,Jindřich Zapletal

By Vladimir Kanovei,Marcin Sabok,Jindřich Zapletal

This publication lays the principles for an exhilarating new zone of analysis in descriptive set conception. It develops a powerful connection among lively subject matters: forcing and analytic equivalence kin. This in flip permits the authors to enhance a generalization of classical Ramsey concept. Given an analytic equivalence relation on a Polish house, can one discover a huge subset of the distance on which it has an easy shape? The e-book offers many confident and damaging normal solutions to this question. The proofs characteristic right forcing and Gandy–Harrington forcing, in addition to partition arguments. the consequences comprise robust canonization theorems for lots of periods of equivalence family and sigma-ideals, in addition to ergodicity leads to situations the place canonization theorems are most unlikely to accomplish. excellent for graduate scholars and researchers in set idea, the booklet presents an invaluable springboard for additional research.

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