Proper ForcingSpringer-Verlag, 1982 - 496 Seiten 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).--Provided by publisher. |
Inhalt
maximal with this property We prove using MA every mad set has cardi | 2 |
2 The consistency of CH | 7 |
On the consistency | 14 |
Urheberrecht | |
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A₁ Aronszajn tree assume Axiom B₁ B₂ belong C₁ canonical name Claim clearly closed unbounded subset cofinality collapse compatible contradiction countable set covering lemma covering model define by induction Definition denote dense subset equivalent Fact filter finite subset forcing notion function F hence holds implies infinite isomorphism iterated forcing large cardinal Levi collapse limit ordinal maximal antichain measurable cardinal N₁ N₂ P-name P-point P₁ P₂ pairwise disjoint partial order player I chooses player II wins Pn+1 poset predense preserved Proof proper forcing prove Q satisfies q₁ Ramsey ultrafilter RCS iteration regular cardinal Remark S₁ satisfies the c.c.c. semi-proper sequence Shelah Souslin stationary subset strongly inaccessible subset of w₁ suffices Suppose T₁ T₂ Theorem trivial ultrafilter uncountable upper bound w-sequence w₂ winning strategy