How many normal measures can ℵω+1 carry?
Arthur W. Apter
Fundamenta Mathematicae, Tome 189 (2006), p. 57-66 / Harvested from The Polish Digital Mathematics Library
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We show that assuming the consistency of a supercompact cardinal with a measurable cardinal above it, it is possible for ℵω+1 to be measurable and to carry exactly τ normal measures, where τ≥ℵω+2 is any regular cardinal. This contrasts with the fact that assuming AD + DC, ℵω+1 is measurable and carries exactly three normal measures. Our proof uses the methods of [6], along with a folklore technique and a new method due to James Cummings.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:282648 
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Arthur W. Apter. How many normal measures can $ℵ_{ω+1}$ carry?. Fundamenta Mathematicae, Tome 189 (2006) pp. 57-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-4/