Department of Mathematics, Baruch College of CUNY, New York, New York 10010, E-mail: AWABB@CUNYVM.CUNY.EDU
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.
(Received July 12 1994)
(Revised February 06 1995)