03591nam 2200673Ia 450 991045556520332120200520144314.01-282-72287-597866127228753-11-021317-610.1515/9783110213171(CKB)2500000000002751(EBL)570603(OCoLC)659500679(SSID)ssj0000433461(PQKBManifestationID)11325377(PQKBTitleCode)TC0000433461(PQKBWorkID)10390714(PQKB)10490502(MiAaPQ)EBC570603(DE-B1597)35729(OCoLC)680619899(OCoLC)979582164(DE-B1597)9783110213171(Au-PeEL)EBL570603(CaPaEBR)ebr10408301(CaONFJC)MIL272287(EXLCZ)99250000000000275120100405d2010 uy 0engur|||||||||||txtccrThe axiom of determinacy, forcing axioms, and the nonstationary ideal[electronic resource] /W. Hugh Woodin2nd rev. ed.Berlin ;New York De Gruyterc20101 online resource (858 p.)De Gruyter series in logic and its applications,1438-1893 ;1Description based upon print version of record.3-11-019702-2 Includes bibliographical references and index. 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 -- BackmatterThe 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. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of Ω-logic and related matters. De 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)1037435MiAaPQMiAaPQMiAaPQBOOK9910455565203321The axiom of determinacy, forcing axioms, and the nonstationary ideal2458417UNINA