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  3. Forcing Idealized
  • Cited by 43
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2008
Online ISBN:
9780511542732
DOI:
https://doi.org/10.1017/CBO9780511542732
Subjects:
Mathematics (general), Mathematics, Logic, Categories and Sets, Algebra
Series:
Cambridge Tracts in Mathematics (174)
Information

Book description

Descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis and measure theory.

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