Proper forcing

by Shelah, Saharon

Type Book

Rate 0.0 /5

Details

Files

Reviews

Download

Title Statements

Full title :Proper forcing / Saharon Shelah.

Summary

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 ʹ1-5 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).

Edition Statements

Publication Date:1982.

Publication Statements

Publisher(s):Springer-Verlag
Place of Publication:Berlin
Language:eng
Publication Date:1982.

The Physical Object

Description:1 online resource (xxix, 496 pages)

Edition Identifiers

ISBN:9783662215432, 3662215438
oclc:ocn298064477
LC Classification:QA3
Dewey Decimal:511.3

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 -…

Subjects

Axiomatic set theory Forcing Forcing (Model theory) Forcing (modeltheorie) Forcing (Théorie des modèles) Kardinalzahl Mengenlehre Modeltheorie Théorie axiomatique des ensembles Verzamelingen (wiskunde)