Canonical Ramsey Theory on Polish Spaces

Name: Canonical Ramsey Theory on Polish Spaces
SKU: 21249332
Price: 341.00 NZD
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Hardback

Series:

Cambridge Tracts in Mathematics

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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.

Author Biography:

Vladimir Kanovei is a mathematician working in descriptive set theory and non-standard analysis. He is Leading Researcher in the Institute for Information Transmission Problems (IITP), Moscow, and Professor at Moscow State University of Railway Engineering (MIIT). Marcin Sabok works in mathematical logic and, in particular, in descriptive set theory. He received his PhD from Wroclaw University, Poland in 2009 and has held postdoctoral positions at the Kurt Gödel Research Center for Mathematical Logic, Vienna and at the University of Illinois, Urbana-Champaign. Sabok is currently Assistant Professor in the Institute of Mathematics at the Polish Academy of Sciences. Jindřich Zapletal is a mathematician working in set theory. He developed a robust connection between descriptive set theory, abstract analysis and Shelah's method of proper forcing. His main research contributions are collected in the book Forcing Idealized (Cambridge University Press, 2008). Zapletal is Professor of Mathematics at the University of Florida.

Release date NZ

September 12th, 2013

Author

Audience

Professional & Vocational

Illustrations

Worked examples or Exercises; 20 Tables, unspecified

Pages

278

Series

Cambridge Tracts in Mathematics

Dimensions

157x235x19

ISBN-13

9781107026858

Product ID

21249332

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