Author:
Jensen Ronald,Schimmerling Ernest,Schindler Ralf,Steel John
Abstract
AbstractWe show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal κ ≥ ℵ such that □κ and □(κ) fail. 2) There is a cardinal κ such that κ is weakly compact in the generic extension by Col(κ, κ+). Of special interest is 1) with κ = ℵ3 since it follows from PFA by theorems of Todorcevic and Velickovic. Our main new technical result, which is due to the first author, is a weak covering theorem for the model obtained by stacking mice over Kc∥κ.
Publisher
Cambridge University Press (CUP)
Reference24 articles.
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4. Steel J. , The derived model theorem, preprint, math.berkeley.edu/~steel/papers/Publications.html.
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