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September 2013 Forcing closed unbounded subsets of $\aleph_{\omega_{1}+1}$
M. C. Stanley
J. Symbolic Logic 78(3): 681-707 (September 2013). DOI: 10.2178/jsl.7803010

Abstract

Using square sequences, a stationary subset $S_T$ of $\aleph_{\omega_{1}+1}$ is constructed from a tree $T$ of height $\omega_1$, uniformly in $T$. Under suitable hypotheses, adding a closed unbounded subset to $S_T$ requires adding a cofinal branch to $T$ or collapsing at least one of $\omega_1$, $\aleph_{\omega_{1}}$, and $\aleph_{\omega_1+1}$. An application is that in ZFC there is no parameter free definition of the family of subsets of $\aleph_{\omega_1+1}$ that have a closed unbounded subset in some $\omega_1$, $\aleph_{\omega_{1}}$, and $\aleph_{\omega_1+1}$ preserving outer model.

Citation

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M. C. Stanley. "Forcing closed unbounded subsets of $\aleph_{\omega_{1}+1}$." J. Symbolic Logic 78 (3) 681 - 707, September 2013. https://doi.org/10.2178/jsl.7803010

Information

Published: September 2013
First available in Project Euclid: 6 January 2014

zbMATH: 1348.03043
MathSciNet: MR3135494
Digital Object Identifier: 10.2178/jsl.7803010

Subjects:

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 3 • September 2013
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