The Journal of Symbolic Logic

Research Article

AD and patterns of singular cardinals below Θ

Arthur W. Apter

Department of Mathematics, Baruch College of CUNY, New York, New York 10010, E-mail: AWABB@CUNYVM.CUNY.EDU

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.

(Received July 12 1994)

(Revised February 06 1995)