Translator Disclaimer
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 ω N ⊂ 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 𝒯 on K such that 𝒯 has successor length and ℳ𝒯 = KN. Moreover, if there exists an elementary embedding π : V → N then the iteration map associated to the main branch of 𝒯 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.

Citation

Download Citation

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

Keywords: core models , large cardinals , Set theory

Rights: Copyright © 2006 Association for Symbolic Logic

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.71 • No. 1 • March 2006
Back to Top