Forcing Closed Unbounded Subsets of אω1+1
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AbstractUsing square sequences, a stationary subset ST of אω1+1 is constructed from a tree T of height ω1, uniformly in T. Under suitable hypotheses, adding a closed unbounded subset to ST requires adding a cofinal branch to T or collapsing at least one of ω1, אω1, and אω1+1. An application is that in ZFC there is no parameter free definition of the family of subsets of אω1+1 that have a closed unbounded subset in some ω1, אω1, and אω1+1 preserving outer model.
2021 ◽
pp. tobaccocontrol-2020-056145
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2002 ◽
Vol 33
(1)
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pp. 23-34
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1966 ◽
Vol 66
(15)
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pp. 377-392
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2009 ◽
Vol 90
(2)
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pp. 227-230
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2013 ◽
Vol 23
(06)
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pp. 1431-1467
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