Journal of Symbolic Logic

Approachability at the second successor of a singular cardinal

Moti Gitik and John Krueger

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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.

Article information

Source
J. Symbolic Logic, Volume 74, Issue 4 (2009), 1211-1224.

Dates
First available in Project Euclid: 5 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1254748688

Digital Object Identifier
doi:10.2178/jsl/1254748688

Mathematical Reviews number (MathSciNet)
MR2583817

Zentralblatt MATH identifier
1184.03046

Subjects
Primary: 03E05: Other combinatorial set theory 03E35: Consistency and independence results

Keywords
approachability ideal internally approachable

Citation

Gitik, Moti; Krueger, John. Approachability at the second successor of a singular cardinal. J. Symbolic Logic 74 (2009), no. 4, 1211--1224. doi:10.2178/jsl/1254748688. https://projecteuclid.org/euclid.jsl/1254748688


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