Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model

Schimmerling, Ernest

doi:10.1090/S0002-9939-02-06455-9

Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model
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Proc. Amer. Math. Soc. 130 (2002), 3385-3391 Request permission

Abstract:

Theorem 4 is a characterization of Woodin cardinals in terms of Skolem hulls and Mostowski collapses. We define weakly hyper-Woodin cardinals and hyper-Woodin cardinals. Theorem 5 is a covering theorem for the Mitchell-Steel core model, which is constructed using total background extenders. Roughly, Theorem 5 states that this core model correctly computes successors of hyper-Woodin cardinals. Within the large cardinal hierarchy, in increasing order we have: measurable Woodin, weakly hyper-Woodin, Shelah, hyper-Woodin, and superstrong cardinals. (The comparison of Shelah versus hyper-Woodin is due to James Cummings.)

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