Iterates of the Core Model

Journal of Symbolic Logic 71 (1):241 - 251 (2006)

Abstract
Let N be a transitive model of ZFC such that ωN ⊂ N and P(R) ⊂ N. Assume that both V and N satisfy "the core model K exists." Then KN is an iterate of K. i.e., there exists an iteration tree J on K such that J has successor length and $\mathit{M}_{\infty}^{\mathit{J}}=K^{N}$. Moreover, if there exists an elementary embedding π: V → N then the iteration map associated to the main branch of J equals π ↾ K. (This answers a question of W. H. Woodin, M. Gitik, and others.) The hypothesis that P(R) ⊂ N is not needed if there does not exist a transitive model of ZFC with infinitely many Woodin cardinals
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DOI 10.2178/jsl/1140641172
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References found in this work BETA

Inner Models in the Region of a Woodin Limit of Woodin Cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
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.
The Core Model for Almost Linear Iterations.Ralf-Dieter Schindler - 2002 - Annals of Pure and Applied Logic 116 (1-3):205-272.

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Citations of this work BETA

Forcing Absoluteness and Regularity Properties.Daisuke Ikegami - 2010 - Annals of Pure and Applied Logic 161 (7):879-894.
The Structure of the Mitchell Order – II.Omer Ben-Neria - 2015 - Annals of Pure and Applied Logic 166 (12):1407-1432.
Core Models in the Presence of Woodin Cardinals.Ralf Schindler - 2006 - Journal of Symbolic Logic 71 (4):1145 - 1154.
Homogeneously Suslin Sets in Tame Mice.Farmer Schlutzenberg - 2012 - Journal of Symbolic Logic 77 (4):1122-1146.

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