Ernest Schimmerling, John R. Steel
Published 1997-02-18Version 1
If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K computes successors of weakly compact cardinals correctly. o K^c is an iterate of K. o (with Mitchell) If alpha is a cardinal > aleph_1, then K-restriction-alpha is universal for mice of height alpha. Other results in this paper, when combined with work of Woodin, imply: o If square-kappa-finite fails and kappa is a singular, strong limit cardinal, then Inductive Determinacy holds. o If square-kappa-finite fails and kappa is a weakly compact cardinal, then L(R)-determinacy holds.
Iterations of V and the core model
On a relation between $λ$-full well-ordered sets and weakly compact cardinals
The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $θ$-supercompact
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