## Journal of Symbolic Logic

### Namba forcing and no good scale

John Krueger

#### 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

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