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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The maximality of the core model


Authors: E. Schimmerling and J. R. Steel
Journal: Trans. Amer. Math. Soc. 351 (1999), 3119-3141
MSC (1991): Primary 03E35, 03E45, 03E55
Published electronically: March 29, 1999
MathSciNet review: 1638250
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Abstract: Our main results are: 1) every countably certified extender that coheres with the core model $K$ is on the extender sequence of $K$, 2) $K$ computes successors of weakly compact cardinals correctly, 3) every model on the maximal 1-small construction is an iterate of $K$, 4) (joint with W. J. Mitchell) $K\|\kappa$ is universal for mice of height $\le\kappa$ whenever $\kappa\geq\aleph _2$, 5) if there is a $\kappa$ such that $\kappa$ is either a singular countably closed cardinal or a weakly compact cardinal, and $\square _\kappa^{<\omega}$ fails, then there are inner models with Woodin cardinals, and 6) an $\omega$-Erdös cardinal suffices to develop the basic theory of $K$.


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Additional Information

E. Schimmerling
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
Address at time of publication: Mathematical Sciences Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Email: eschimme@andrew.cmu.edu

J. R. Steel
Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
Email: steel@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02411-3
PII: S 0002-9947(99)02411-3
Keywords: Large cardinals, core models
Received by editor(s): May 17, 1997
Received by editor(s) in revised form: October 25, 1997
Published electronically: March 29, 1999
Additional Notes: This research was partially supported by the NSF
Article copyright: © Copyright 1999 American Mathematical Society