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100   $a20100405d2010      uy         0
101 0 $aeng
135   $aur|||||||||||
181   $ctxt
182   $cc
183   $acr
200 14$aThe axiom of determinacy, forcing axioms, and the nonstationary ideal /$fW. Hugh Woodin
205   $a2nd rev. ed.
210   $aBerlin ;$aNew York $cDe Gruyter$dc2010
215   $a1 online resource (858 p.)
225 1 $aDe Gruyter series in logic and its applications,$x1438-1893 ;$v1
300   $aDescription based upon print version of record.
311   $a3-11-019702-2 
320   $aIncludes bibliographical references and index.
327   $t Frontmatter -- $tContents -- $t1 Introduction -- $t2 Preliminaries -- $t3 The nonstationary ideal -- $t4 The ?max-extension -- $t5 Applications -- $t6 ?max variations -- $t7 Conditional variations -- $t8 ? principles for ? 1 -- $t9 Extensions of L(?, ?) -- $t10 Further results -- $t11 Questions -- $t Backmatter
330   $aThe starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on ?1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of ?-logic and related matters. 
410  0$aDe Gruyter series in logic and its applications ;$v1.
606   $aForcing (Model theory)
606   $aModel theory
615  0$aForcing (Model theory)
615  0$aModel theory.
676   $a511.3
686   $aSK 130$2rvk
700   $aWoodin$b W. H$g(W. Hugh)$01676850
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910806265303321
996   $aThe axiom of determinacy, forcing axioms, and the nonstationary ideal$94043318
997   $aUNINA