The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal / / W. Hugh Woodin.
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Superior document: | Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999 |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2013] ©1999 |
Year of Publication: | 2013 |
Edition: | Reprint 2011 |
Language: | English |
Series: | De Gruyter Series in Logic and Its Applications ,
1 |
Online Access: | |
Physical Description: | 1 online resource (934 p.) |
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Other title: | Frontmatter -- 1 Introduction -- 2 Preliminaries -- 3 The nonstationary ideal -- 4 The ℙmax-extension -- 5 Applications -- 6 ℙmax variations. 6.1 2ℙmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.1 ℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.2 ℚ*max -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.3 2ℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.4 Weak Kurepa trees and ℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.5 KTℚmax -- 6 ℙmax variations. 6.2 Variations for obtaining ω1-dense ideals. 6.2.6 Null sets and the nonstationary ideal -- 6 ℙmax variations. 6.3 Nonregular ultrafilters on ω1 -- 7 Conditional variations -- 8 ♣ principles for ω1. 8.1 Condensation Principles -- 8 ♣ principles for ω1. 8.2 ℙ♣NSmax -- 8 ♣ principles for ω1. 8.3 The principles, ♣+NS and ♣++NS -- 9 Extensions of L(Γ, ℝ). 9.1 AD+ -- 9 Extensions of L(Γ, ℝ). 9.2 The ℙmax-extension of L(Γ, ℝ) -- 9 Extensions of L(Γ, ℝ). 9.3 The ℚmax-extension of L(Γ, ℝ) -- 9 Extensions of L(Γ, ℝ). 9.4 Chang’s Conjecture -- 9 Extensions of L(Γ, ℝ). 9.5 Weak and Strong Reflection Principles -- 9 Extensions of L(Γ, ℝ). 9.6 Strong Chang’s Conjecture -- 9 Extensions of L(Γ, ℝ). 9.7 Ideals on ω2 -- 10 Further results. 10.1 Forcing notions and large cardinals -- 10 Further results. 10.2 Coding into L(P(ω1)) -- 10 Further results. 10.3 Bounded forms of Martin’s Maximum -- 10 Further results. 10.4 Ω-logic -- 10 Further results. 10.5 Ω-logic and the Continuum Hypothesis -- 10 Further results. 10.6 The Axiom (*)+ -- 10 Further results. 10.7 The Effective Singular Cardinals Hypothesis -- 11 Questions -- Bibliography -- Index |
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Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110804737 9783110637199 9783110233957 |
ISSN: | 1438-1893 ; |
DOI: | 10.1515/9783110804737 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | W. Hugh Woodin. |