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 | References | Similar Articles | Additional Information

Abstract: Our main results are: 1) every countably certified extender that coheres with the core model is on the extender sequence of , 2) computes successors of weakly compact cardinals correctly, 3) every model on the maximal 1-small construction is an iterate of , 4) (joint with W. J. Mitchell) is universal for mice of height whenever , 5) if there is a such that is either a singular countably closed cardinal or a weakly compact cardinal, and fails, then there are inner models with Woodin cardinals, and 6) an -Erdös cardinal suffices to develop the basic theory of .

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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:
https://doi.org/10.1090/S0002-9947-99-02411-3

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