. L O ] 1 5 Ju l 1 99 7 Not collapsing cardinals ≤ κ in ( < κ ) – support iterations : Part
نویسنده
چکیده
We deal with the problem of preserving various versions of completeness in (< κ)–support iterations of forcing notions, generalizing the case “S–complete proper is preserved by CS iterations for a stationary costationary S ⊆ ω1”. We give applications to Uniformization and the Whitehead problem. In particular, for a strongly inaccessible cardinal κ and a stationary set S ⊆ κ with fat complement we can have uniformization for 〈Aδ : δ ∈ S〉, Aδ ⊆ δ = supAδ, cf(δ) = otp(Aδ) and a stationary non-reflecting set S ⊆ S. ∗ Research supported by German-Israeli Foundation for Scientific Research & Development Grant No. G-294.081.06/93 and by The National Science Foundation Grant No. 144–EF67. Publication No 587.
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