How many normal measures can $ℵ_{ω+1}$ carry?

• Autorzy: Arthur W. Apter
• Języki publikacji: EN

Abstrakty

EN

We show that assuming the consistency of a supercompact cardinal with a measurable cardinal above it, it is possible for $ℵ_{ω+1}$ to be measurable and to carry exactly τ normal measures, where $τ ≥ ℵ_{ω+2}$ is any regular cardinal. This contrasts with the fact that assuming AD + DC, ${ℵ_{ω+1}}$ 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.

Kategorie tematyczne

• 03E55: Large cardinals
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 191
• Numer: 1
• Strony: 57-66

Daty

wydano

2006

Twórcy

autor

Arthur W. Apter

• Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.

Identyfikatory

DOI

10.4064/fm191-1-4