000 | 05596nam a22004695i 4500 | ||
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001 | 978-3-662-21543-2 | ||
003 | DE-He213 | ||
005 | 20190213151637.0 | ||
007 | cr nn 008mamaa | ||
008 | 131202s1982 gw | s |||| 0|eng d | ||
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_a9783662215432 _9978-3-662-21543-2 |
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024 | 7 |
_a10.1007/978-3-662-21543-2 _2doi |
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050 | 4 | _aQA8.9-10.3 | |
072 | 7 |
_aPBC _2bicssc |
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072 | 7 |
_aMAT018000 _2bisacsh |
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_aPBC _2thema |
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072 | 7 |
_aPBCD _2thema |
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082 | 0 | 4 |
_a511.3 _223 |
100 | 1 |
_aShelah, Saharon. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aProper Forcing _h[electronic resource] / _cby Saharon Shelah. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1982. |
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300 |
_aXXXII, 500 p. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v940 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-662-21543-2 |
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