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Medientyp:
E-Artikel
Titel:
Jónsson Cardinals, Erdös Cardinals, and the Core Model
Beteiligte:
Mitchell, W. J.
Erschienen:
The Association for Symbolic Logic, Inc., 1999
Erschienen in:The Journal of Symbolic Logic
Sprache:
Englisch
ISSN:
0022-4812
Entstehung:
Anmerkungen:
Beschreibung:
<p>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 <tex-math>$\subset$</tex-math> κ and κ is regular, then L<sub>κ</sub>[A] is a Jónsson algebra. The proof of this result, Lemma 2.5, is very short and entirely elementary.</p>