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June 2003 A Gitik iteration with nearly Easton factoring
William J. Mitchell
J. Symbolic Logic 68(2): 481-502 (June 2003). DOI: 10.2178/jsl/1052669060

Abstract

We reprove Gitik’s theorem that if the GCH holds and $o(\gk)=\gk+1$ then there is a generic extension in which $\gk$ is still measurable and there is a closed unbounded subset C of $\gk$ such that every $ν\in C$ is inaccessible in the ground model. Unlike the forcing used by Gitik, the iterated forcing $\radin\gl+1$ used in this paper has the property that if $\gl$ is a cardinal less then $\gk$ then $\radin\gl+1$ can be factored in V as $\radin\gk+1=\radin\gl+1\times\radin\gl+1,\gk$ where $\card{\radin\gl+1}\le\gl+$ and $\radin\gl+1,\gk$ does not add any new subsets of $\gl$.

Citation

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William J. Mitchell. "A Gitik iteration with nearly Easton factoring." J. Symbolic Logic 68 (2) 481 - 502, June 2003. https://doi.org/10.2178/jsl/1052669060

Information

Published: June 2003
First available in Project Euclid: 11 May 2003

zbMATH: 1059.03052
MathSciNet: MR1976587
Digital Object Identifier: 10.2178/jsl/1052669060

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.68 • No. 2 • June 2003
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