The maximality of the core model
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- by E. Schimmerling and J. R. Steel PDF
- Trans. Amer. Math. Soc. 351 (1999), 3119-3141 Request permission
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 $K$.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 3119-3141
- MSC (1991): Primary 03E35, 03E45, 03E55
- DOI: https://doi.org/10.1090/S0002-9947-99-02411-3
- MathSciNet review: 1638250