Approachability at the second successor of a singular cardinal
Moti Gitik and John Krueger
Source: J. Symbolic Logic Volume 74, Issue 4 (2009), 1211-1224.
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.
Primary Subjects: 03E05, 03E35
Keywords: approachability ideal; internally approachable
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1254748688
Digital Object Identifier: doi:10.2178/jsl/1254748688
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