Annals of Pure and Applied Logic 158 (1-2):40-57 (2009)

We give some applications of mixed support forcing iterations to the topics of disjoint stationary sequences and internally approachable sets. In the first half of the paper we study the combinatorial content of the idea of a disjoint stationary sequence, including its relation to adding clubs by forcing, the approachability ideal, canonical structure, the proper forcing axiom, and properties related to internal approachability. In the second half of the paper we present some consistency results related to these ideas. We construct a model in which a disjoint stationary sequence exists at the successor of an arbitrary regular uncountable cardinal. We also construct models in which the properties of being internally stationary, internally club, and internally approachable are distinct
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DOI 10.1016/j.apal.2008.09.024
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References found in this work BETA

Reflecting Stationary Sets and Successors of Singular Cardinals.Saharon Shelah - 1991 - Archive for Mathematical Logic 31 (1):25-53.
Aronszajn Trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
Forcing Closed Unbounded Sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.

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Citations of this work BETA

A General Mitchell Style Iteration.John Krueger - 2008 - Mathematical Logic Quarterly 54 (6):641-651.
Approachability at the Second Successor of a Singular Cardinal.Moti Gitik & John Krueger - 2009 - Journal of Symbolic Logic 74 (4):1211 - 1224.
Forcing Axioms, Approachability, and Stationary Set Reflection.Sean D. Cox - 2021 - Journal of Symbolic Logic 86 (2):499-530.

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