Journal of Symbolic Logic

Namba forcing and no good scale

John Krueger

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Abstract

We develop a version of Namba forcing which is useful for constructing models with no good scale on $\aleph_\omega$. A model is produced in which $\Box_{\aleph_n}$ holds for all finite $n \ge 1$, but there is no good scale on $\aleph_\omega$; this strengthens a theorem of Cummings, Foreman, and Magidor [3] on the non-compactness of square.

Article information

Source
J. Symbolic Logic, Volume 78, Issue 3 (2013), 785-802.

Dates
First available in Project Euclid: 6 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1389032275

Digital Object Identifier
doi:10.2178/jsl.7803050

Mathematical Reviews number (MathSciNet)
MR3135498

Zentralblatt MATH identifier
1315.03085

Keywords
Good scale Namba forcing

Citation

Krueger, John. Namba forcing and no good scale. J. Symbolic Logic 78 (2013), no. 3, 785--802. doi:10.2178/jsl.7803050. https://projecteuclid.org/euclid.jsl/1389032275


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