How many normal measures can ℵmath image carry?



Relative to the existence of a supercompact cardinal with a measurable cardinal above it, we show that it is consistent for ℵ1 to be regular and for ℵmath image to be measurable and to carry precisely τ normal measures, where τ ≥ ℵmath image is any regular cardinal. This extends the work of [2], in which the analogous result was obtained for ℵω +1 using the same hypotheses (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)