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

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Reflecting Stationary Sets and Successors of Singular Cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.
Notes on Singular Cardinal Combinatorics.James Cummings - 2005 - Notre Dame Journal of Formal Logic 46 (3):251-282.
A General Mitchell Style Iteration.John Krueger - 2008 - Mathematical Logic Quarterly 54 (6):641-651.

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