Ad and Patterns of Singular Cardinals Below $\Theta$
Apter, Arthur W.
J. Symbolic Logic, Tome 61 (1996) no. 1, p. 225-235 / Harvested from Project Euclid
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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 $\aleph_1$.
Publié le : 1996-03-14
Classification:  
@article{1183744935,
     author = {Apter, Arthur W.},
     title = {Ad and Patterns of Singular Cardinals Below $\Theta$},
     journal = {J. Symbolic Logic},
     volume = {61},
     number = {1},
     year = {1996},
     pages = { 225-235},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183744935}
}

Apter, Arthur W. Ad and Patterns of Singular Cardinals Below $\Theta$. J. Symbolic Logic, Tome 61 (1996) no. 1, pp.  225-235. http://gdmltest.u-ga.fr/item/1183744935/