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The self-iterability of L[E]

Published online by Cambridge University Press:  12 March 2014

Ralf Schindler  and
John Steel
Ralf Schindler
Affiliation:
Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany, E-mail: rds@uni-muenster.de
John Steel
Affiliation:
Department of Mathematics, 717 Evans Hall, University of California, Berkeley, Ca 94720, USA, E-mail: steel@math.berkeley.edu
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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 κ which is not a limit of Woodin cardinals there is some cutpoint t < κ such that Jκ[E] is iterable above t with respect to iteration trees of length less than κ.

As an application we show L[E] to be a model of the following two cardinals versions of the diamond principle. If λ > κ > ω1 are cardinals, then holds true, and if in addition λ is regular, then holds true.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 751 - 779
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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