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AD and patterns of singular cardinals below Θ

  • Arthur W. Apter (a1)

Abstract

Using Steel's recent result that assuming AD, in L[ℝ] below Θ, κ is regular iff κ is measurable, we mimic below Θ certain earlier results of Gitik. In particular, we construct via forcing a model in which all uncountable cardinals below Θ are singular and a model in which the only regular uncountable cardinal below Θ is ℵ1.

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[20]Steel, J., paper 1, in preparation.
[21]Steel, J., paper 2, in preparation.

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AD and patterns of singular cardinals below Θ

  • Arthur W. Apter (a1)

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