Proper forcing / / Saharon Shelah

• Autore: Shelah Saharon
• Pubblicazione: Berlin ; ; Heidelberg : , : Springer-Verlag, , [1982]; ©1982
• Edizione: 1st ed. 1982.
• Descrizione fisica: 1 online resource (XXXII, 500 p.)
• Disciplina: 511.3
• Soggetto topico: Forcing (Model theory)
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: 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 -- ?-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.
• Sommario/riassunto: 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).
• Titolo autorizzato: Proper forcing
• ISBN: 3-662-21543-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466380503316
• Lo trovi qui: Univ. di Salerno
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 940