Journal of Symbolic Logic 64 (3):1065-1086 (1999)

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 δ-Erdös in K. In the absence of the Steel core model K we prove the same conclusion for any model L[E] such that either V = L[E] 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[E]. The proof includes one lemma of independent interest: If V = L[A], where A $\subset$ 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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DOI 10.2307/2586619
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References found in this work BETA

The Core Model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
The Covering Lemma Up to a Woodin Cardinal.W. J. Mitchell, E. Schimmerling & J. R. Steel - 1997 - Annals of Pure and Applied Logic 84 (2):219-255.
Ramsey Cardinals and Constructibility.William Mitchell - 1979 - Journal of Symbolic Logic 44 (2):260-266.

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Large Cardinals, Inner Models, and Determinacy: An Introductory Overview.P. D. Welch - 2015 - Notre Dame Journal of Formal Logic 56 (1):213-242.

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