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Jónsson cardinals, Erdős cardinals, and the core model

Published online by Cambridge University Press:  12 March 2014

W. J. Mitchell
W. J. Mitchell*
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, Florida 32611-8105, USA E-mail: mitchell@math.ufl.edu
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Abstract

We show that if there is no inner model with a Woodin cardinal and the Steel core model K exists, then every Jónsson cardinal is Ramsey in K, and every δ-Jónsson cardinal is δ5-Erdős in K.

In the absence of the Steel core model K we prove the same conclusion for any model L[] such that either V = L[] is the minimal model for a Woodin cardinal, or there is no inner model with a Woodin cardinal and V is a generic extension of L[].

The proof includes one lemma of independent interest: If V = L[A], where A ⊂ κ and κ is regular, then Lκ[A] is a Jónsson algebra. The proof of this result. Lemma 2.5, is very short and entirely elementary.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 3 , September 1999 , pp. 1065 - 1086
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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