Approachability at the Second Successor of a Singular Cardinal

Journal of Symbolic Logic 74 (4):1211 - 1224 (2009)

Abstract
We prove that if μ is a regular cardinal and ℙ is a μ-centered forcing poset, then ℙ forces that $(I[\mu ^{ + + } ])^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
Keywords approachability ideal   internally approachable
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DOI 10.2178/jsl/1254748688
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