## Journal of Symbolic Logic

### Ad and Patterns of Singular Cardinals Below $\Theta$

Arthur W. Apter

#### Abstract

Using Steel's recent result that assuming AD, in $L\lbrack\mathbb{R}\rbrack$ below $\Theta, \kappa$ is regular $\operatorname{iff} \kappa$ is measurable, we mimic below $\Theta$ certain earlier results of Gitik. In particular, we construct via forcing a model in which all uncountable cardinals below $\Theta$ are singular and a model in which the only regular uncountable cardinal below $\Theta$ is $\aleph_1$.

#### Article information

Source
J. Symbolic Logic, Volume 61, Issue 1 (1996), 225-235.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183744935

Mathematical Reviews number (MathSciNet)
MR1380685

Zentralblatt MATH identifier
0855.03029

JSTOR
Apter, Arthur W. Ad and Patterns of Singular Cardinals Below $\Theta$. J. Symbolic Logic 61 (1996), no. 1, 225--235. https://projecteuclid.org/euclid.jsl/1183744935