The self-iterability of L[E]

Journal of Symbolic Logic 74 (3):751-779 (2009)
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Abstract

Let L[E] be an iterable tame extender model. We analyze to which extent L[E] knows fragments of its own iteration strategy. Specifically, we prove that inside L[E], for every cardinal K which is not a limit of Woodin cardinals there is some cutpoint t K > a>ω1 are cardinals, then ◊$_{K.\lambda }^* $ holds true, and if in addition λ is regular, then ◊$_{K.\lambda }^* $ holds true

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Author Profiles

Jack Steel
University of Edinburgh

References found in this work

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.

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