Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model
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- by Ernest Schimmerling PDF
- 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.)References
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Additional Information
- Ernest Schimmerling
- Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
- Email: eschimme@andrew.cmu.edu
- Received by editor(s): May 16, 2001
- Received by editor(s) in revised form: June 14, 2001
- Published electronically: March 18, 2002
- Additional Notes: This research was supported by NSF DMS-0088948.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3385-3391
- MSC (1991): Primary 03E45, 03E55
- DOI: https://doi.org/10.1090/S0002-9939-02-06455-9
- MathSciNet review: 1913018