Forcing closed unbounded subsets of ω2

Annals of Pure and Applied Logic 110 (1-3):23-87 (2001)
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Abstract

It is shown that there is no satisfactory first-order characterization of those subsets of ω 2 that have closed unbounded subsets in ω 1 , ω 2 and GCH preserving outer models. These “anticharacterization” results generalize to subsets of successors of uncountable regular cardinals. Similar results are proved for trees of height and cardinality κ + and for partitions of [ κ + ] 2 , when κ is an infinite cardinal

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10.1016/s0168-0072(00)00062-2

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Citations of this work

Adding Closed Unbounded Subsets of ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.
Forcing Closed Unbounded Subsets of אω1+1.M. C. Stanley - 2013 - Journal of Symbolic Logic 78 (3):681-707.

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References found in this work

Forcing closed unbounded sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Adding a closed unbounded set.J. E. Baumgartner, L. A. Harrington & E. M. Kleinberg - 1976 - Journal of Symbolic Logic 41 (2):481-482.
A non-generic real incompatible with 0#.M. C. Stanley - 1997 - Annals of Pure and Applied Logic 85 (2):157-192.
Cardinal-preserving extensions.Sy D. Friedman - 2003 - Journal of Symbolic Logic 68 (4):1163-1170.
A non-generic real incompatible with 0< sup>#.Maurice C. Stanley - 1997 - Annals of Pure and Applied Logic 85 (2):157-192.

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