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140122  eng 
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a 9783662215432

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1 

a Shelah, S.

245 
0 
0 
a Proper Forcing
h Elektronische Ressource
c by S. Shelah

250 


a 1st ed. 1982

260 


a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 1982, 1982

300 


a XXXII, 500 p
b online resource

505 
0 

a Reflection properties of S 02: Refining Avraham's problem and precipitous ideals  Strong preservation and semiproperness  Friedman's problem  The theorems  The condition  The preservation properties guaranteed by the Scondition  Forcing notions satisfying the Scondition  Finite composition  Preservation of the Icondition by iteration  Further independence results  0 Introduction  When is Namba forcing semiproper, Chang Conjecture and games  Games and properness  Amalgamating the Scondition 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  Unifstrong negation of the weak diamond  On the power of Ext and Whitehead problem  Weak diamond for ?2 assuming CH.

505 
0 

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(Ppoint) property  There may be no Ppoint  There may exist a unique Ramsey ultrafilter  On the ?2chain 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  Pseudocompleteness  Specific forcings  Chain conditions and Avraham's problem 

505 
0 

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 ?2Aronszajn 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 

653 


a Mathematical logic

653 


a Mathematical Logic and Foundations

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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0 

a Lecture Notes in Mathematics

028 
5 
0 
a 10.1007/9783662215432

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u https://doi.org/10.1007/9783662215432?nosfx=y
x Verlag
3 Volltext

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0 

a 511.3

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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 §15 were lectured on and written up by Shai Ben David. Also our presentation is quite selfcontained. 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)
