The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

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Walter de Gruyter, Jan 1, 1999 - Mathematics - 934 pages
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Identifies a canonical model in which the continuum hypothesis (CH) is false. This model is a forcing extension of L(R) and the method can be varied to produce a wide class of similar models each of which can be viewed as a reduction of this model. Analysis of these models arises from an interplay between ideas from descriptive set theory and from combinatorial set theory. The original motivation for the definition of these models resulted from the discovery that it is possible, in the presence of large cardinals, to force the effective failure of CH. Contains chapters on preliminaries, the nonstationary ideal, the Pmax-extension, application, Pmax variations, conditional variations, and condensation principles. Includes a six-page section of questions and exercises. Annotation copyrighted by Book News, Inc., Portland, OR
  

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Contents

Introduction
1
Preliminaries
18
The nonstationary ideal
48
The Pmaxextension
115
Applications
184
Pmax variations
291
Conditional variations
432
+ principles for b
498
Extensions of LI R
617
Further results
769
Questions
921
Bibliography
927
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