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Forcing Closed Unbounded Subsets of אω1+1

Published online by Cambridge University Press:  12 August 2016

M. C. Stanley
M. C. Stanley*
Affiliation:
Math Department San Jose State, San Jose, Ca 95192, USA, E-mail: [email protected]
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Abstract

Using 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.

Keywords

03E0503E3503E4003E45stationary setclosed unbounded settreesquarestrong coveringpatternforcingclass forcing
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 3 , September 2013 , pp. 681 - 707
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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