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Jónsson cardinals, Erdős cardinals, and the core model

  • W. J. Mitchell (a1)


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 L κ[A] is a Jónsson algebra. The proof of this result. Lemma 2.5, is very short and entirely elementary.



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[10] Steel, John R., The core model iterability problem, Association for Symbolic Logic Notes in Logic, no. 8, Springer-Verlag, 1996.

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Jónsson cardinals, Erdős cardinals, and the core model

  • W. J. Mitchell (a1)


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