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March 2006 Iterates of the core model
Ralf Schindler
J. Symbolic Logic 71(1): 241-251 (March 2006). DOI: 10.2178/jsl/1140641172

Abstract

Let N be a transitive model of ZFC such that Ο‰ N βŠ‚ N and 𝒫(ℝ) βŠ‚ N. Assume that both V and N satisfy β€œthe core model K exists.” Then KN is an iterate of K, i.e., there exists an iteration tree 𝒯 on K such that 𝒯 has successor length and β„³π’―βˆž = KN. Moreover, if there exists an elementary embedding Ο€ : V β†’ N then the iteration map associated to the main branch of 𝒯 equals Ο€ β†Ύ K. (This answers a question of W. H. Woodin, M. Gitik, and others.) The hypothesis that 𝒫(ℝ) βŠ‚ N is not needed if there does not exist a transitive model of ZFC with infinitely many Woodin cardinals.

Citation

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Ralf Schindler. "Iterates of the core model." J. Symbolic Logic 71 (1) 241 - 251, March 2006. https://doi.org/10.2178/jsl/1140641172

Information

Published: March 2006
First available in Project Euclid: 22 February 2006

zbMATH: 1109.03063
MathSciNet: MR2210065
Digital Object Identifier: 10.2178/jsl/1140641172

Subjects:
Primary: 03E15, 03E45, 03E55

Rights: Copyright Β© 2006 Association for Symbolic Logic

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Vol.71 β€’ No. 1 • March 2006
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