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AD and patterns of singular cardinals below Θ

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter
Arthur W. Apter*
Affiliation:
Department of Mathematics, Baruch College of CUNY, New York, New York 10010, E-mail: AWABB@CUNYVM.CUNY.EDU
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 1 , March 1996 , pp. 225 - 235
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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