• 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
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  • 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 &lt;tex-math&gt;$\subset$&lt;/tex-math&gt; κ and κ is regular, then L&lt;sub&gt;κ&lt;/sub&gt;[A] is a Jónsson algebra. The proof of this result, Lemma 2.5, is very short and entirely elementary.</p>