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140122 ||| eng |
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|a 9783662215432
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| 100 |
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|a Shelah, S.
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| 245 |
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|a Proper Forcing
|h Elektronische Ressource
|c by S. Shelah
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| 250 |
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|a 1st ed. 1982
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1982, 1982
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| 300 |
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|a XXXII, 500 p
|b online resource
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| 505 |
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|a 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.
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| 505 |
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|a ?-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 --
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|a Introducing 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 --
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| 653 |
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|a Mathematical logic
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| 653 |
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|a Mathematical Logic and Foundations
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Lecture Notes in Mathematics
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| 028 |
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|a 10.1007/978-3-662-21543-2
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-662-21543-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 511.3
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| 520 |
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|a These 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)
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