03953nam 22006491 450 991046426460332120200520144314.03-11-080473-510.1515/9783110804737(CKB)3390000000033132(SSID)ssj0000559598(PQKBManifestationID)11353402(PQKBTitleCode)TC0000559598(PQKBWorkID)10568090(PQKB)11085561(MiAaPQ)EBC3044462(WaSeSS)Ind00009121(DE-B1597)42217(OCoLC)853247543(OCoLC)857769673(DE-B1597)9783110804737(Au-PeEL)EBL3044462(CaPaEBR)ebr10789491(CaONFJC)MIL810935(OCoLC)922947712(EXLCZ)99339000000003313219990402d1999 uy 0engurcnu||||||||txtccrThe axiom of determinacy, forcing axioms, and the nonstationary ideal /W. Hugh WoodinReprint 2011Berlin ;New York :W. de Gruyter,1999.1 online resource (944 pages)De Gruyter Series in Logic and Its Applications ;1De Gruyter series in logic and its applications ;1Bibliographic Level Mode of Issuance: Monograph3-11-015708-X Includes bibliographical references (pages [927]-929) and index. 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 -- IndexDe Gruyter series in logic and its applications ;1.Forcing (Model theory)Model theoryElectronic books.Forcing (Model theory)Model theory.511.3Woodin W. H(W. Hugh)1037435MiAaPQMiAaPQMiAaPQBOOK9910464264603321The axiom of determinacy, forcing axioms, and the nonstationary ideal2458417UNINA