The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal / / W. Hugh Woodin.

• Superior document: Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999
• VerfasserIn: Woodin, W. Hugh,
• 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
• Physical Description: 1 online resource (934 p.)
• 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
• 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.