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Record Nr. |
UNINA9910806265303321 |
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Autore |
Woodin W. H (W. Hugh) |
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Titolo |
The axiom of determinacy, forcing axioms, and the nonstationary ideal / / W. Hugh Woodin |
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Pubbl/distr/stampa |
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Berlin ; ; New York, : De Gruyter, c2010 |
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ISBN |
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1-282-72287-5 |
9786612722875 |
3-11-021317-6 |
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Edizione |
[2nd rev. ed.] |
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Descrizione fisica |
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1 online resource (858 p.) |
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Collana |
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De Gruyter series in logic and its applications, , 1438-1893 ; ; 1 |
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Classificazione |
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Disciplina |
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Soggetti |
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Forcing (Model theory) |
Model theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- 1 Introduction -- 2 Preliminaries -- 3 The nonstationary ideal -- 4 The ℙmax-extension -- 5 Applications -- 6 ℙmax variations -- 7 Conditional variations -- 8 ♣ principles for ω 1 -- 9 Extensions of L(Γ, ℝ) -- 10 Further results -- 11 Questions -- Backmatter |
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Sommario/riassunto |
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The starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on ω1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is directed to researchers and advanced graduate students in Set Theory. |
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