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001 978-3-662-21543-2
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008 131202s1982 gw | s |||| 0|eng d
020 _a9783662215432
_9978-3-662-21543-2
024 7 _a10.1007/978-3-662-21543-2
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aMAT018000
_2bisacsh
072 7 _aPBC
_2thema
072 7 _aPBCD
_2thema
082 0 4 _a511.3
_223
100 1 _aShelah, Saharon.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aProper Forcing
_h[electronic resource] /
_cby Saharon Shelah.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1982.
300 _aXXXII, 500 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v940
505 0 _aIntroducing forcing -- The consistency of CH (the continuum hypothesis) -- On the consistency of the failure of CH -- More on the cardinality and cohen reals -- Equivalence of forcings notions, and canonical names -- Random reals, collapsing cardinals and diamonds -- The composition of two forcing notions -- Iterated forcing -- Martin Axiom and few applications -- The uniformization property -- Maximal almost disjoint families of subset of ? -- Introducing properness -- More on properness -- Preservation of properness under countable support iteration -- Martin Axiom revisited -- On Aronszajn trees -- Maybe there is no ?2-Aronszajn tree -- Closed unbounded subsets of ?1 can run away from many sets -- On oracle chain conditions -- The omitting type theorem -- Iterations of -c.c. forcings -- Reduction of the main theorem to the main lemma -- Proof of main lemma 4.6 -- Iteration of forcing notions which does not add reals -- Generalizations of properness -- ?-properness and (E,?)-properness revisited -- Preservation of ?- properness + the ??- property -- What forcing can we iterate without addding reals -- Specializing an Aronszajn tree without adding reals -- Iteration of orcing notions -- A general preservation theorem -- Three known properties -- The PP(P-point) property -- There may be no P-point -- There may exist a unique Ramsey ultrafilter -- On the ?2-chain condition -- The axioms -- Applications of axiom II -- Application of axiom I -- A counterexample connected to preservation -- Mixed iteration -- Chain conditions revisited -- The axioms revisited -- More on forcing not adding ?-sequences and on the diagonal argument -- Free limits -- Preservation by free limit -- Aronszajn trees: various ways to specialize -- Independence results -- Iterated forcing with RCS (revised countable support) -- Proper forcing revisited -- Pseudo-completeness -- Specific forcings -- Chain conditions and Avraham's problem -- Reflection properties of S 02: Refining Avraham's problem and precipitous ideals -- Strong preservation and semi-properness -- Friedman's problem -- The theorems -- The condition -- The preservation properties guaranteed by the S-condition -- Forcing notions satisfying the S-condition -- Finite composition -- Preservation of the I-condition by iteration -- Further independence results -- 0 Introduction -- When is Namba forcing semi-proper, Chang Conjecture and games -- Games and properness -- Amalgamating the S-condition with properness -- The strong covering lemma: Definition and implications -- Proof of strong covering lemmas -- A counterexample -- When adding a real cannot destroy CH -- Bound on for ?? singular -- Concluding remarks and questions -- Unif-strong negation of the weak diamond -- On the power of Ext and Whitehead problem -- Weak diamond for ?2 assuming CH.
520 _aThese notes can be viewed and used in several different ways, each has some justification, a collection of papers, a research monograph or a text book. The author has lectured variants of several of the chapters several times: in University of California, Berkeley, 1978, Ch. III , N, V in Ohio State Univer­ sity in Columbus, Ohio 1979, Ch. I,ll and in the Hebrew University 1979/80 Ch. I, II, III, V, and parts of VI. Moreover Azriel Levi, who has a much better name than the author in such matters, made notes from the lectures in the Hebrew University, rewrote them, and they ·are Chapters I, II and part of III , and were somewhat corrected and expanded by D. Drai, R. Grossberg and the author. Also most of XI §1-5 were lectured on and written up by Shai Ben David. Also our presentation is quite self-contained. We adopted an approach I heard from Baumgartner and may have been used by others: not proving that forcing work, rather take axiomatically that it does and go ahead to applying it. As a result we assume only knowledge of naive set theory (except some iso­ lated points later on in the book).
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aMathematical Logic and Foundations.
_0http://scigraph.springernature.com/things/product-market-codes/M24005
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662215449
776 0 8 _iPrinted edition:
_z9783540115939
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v940
856 4 0 _uhttps://doi.org/10.1007/978-3-662-21543-2
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
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