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December 2009 Approachability at the second successor of a singular cardinal
Moti Gitik, John Krueger
J. Symbolic Logic 74(4): 1211-1224 (December 2009). DOI: 10.2178/jsl/1254748688

Abstract

We prove that if μ is a regular cardinal and ℛ is a μ-centered forcing poset, then ℛ forces that (I[μ++])V generates I[μ++] modulo clubs. Using this result, we construct models in which the approachability property fails at the successor of a singular cardinal. We also construct models in which the properties of being internally club and internally approachable are distinct for sets of size the successor of a singular cardinal.

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Moti Gitik. John Krueger. "Approachability at the second successor of a singular cardinal." J. Symbolic Logic 74 (4) 1211 - 1224, December 2009. https://doi.org/10.2178/jsl/1254748688

Information

Published: December 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1184.03046
MathSciNet: MR2583817
Digital Object Identifier: 10.2178/jsl/1254748688

Subjects:
Primary: 03E05, 03E35

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 4 • December 2009
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