Proper and Improper Forcing |
Contents
Introduction | xv |
Forcing Basic Facts | xxvi |
3 Canonical Functions for wi 829 | xlv |
Copyright | |
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A₁ adding reals Aronszajn tree assume Axiom B₁ belongs C₁ cf(a Claim clause clearly cofinality collapse compatible condition countable set countable support covering model define by induction Definition dense subset disjoint Dom(ƒ elementary submodel filter finite forcing notion function hence holds implies induction hypothesis infinite initial segment iterated forcing Lemma lg(n lim(T limit ordinal maximal antichain N₁ N1-complete N₂ Note P-name P-point P₁ pairwise partial order player I chooses player II wins Pn+1 pre-dense subset preservation Proof proper forcing prove regular cardinal Remark S₁ satisfies the c.c.c. satisfies the K-c.c semiproper sequence Skolem Hull stationary subset strongly inaccessible subset of w₁ successor ordinal Suppose T₁ Theorem trivial ultrafilter Un<w uncountable upper bound w₂ winning strategy