Ad and Patterns of Singular Cardinals Below $\Theta$

Journal of Symbolic Logic 61 (1):225-235 (1996)
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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 $\aleph_1$.

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