Strong compactness, measurability, and the class of supercompact cardinals

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

Abstrakty

EN

We prove two theorems concerning strong compactness, measurability, and the class of supercompact cardinals. We begin by showing, relative to the appropriate hypotheses, that it is consistent non-trivially for every supercompact cardinal to be the limit of (non-supercompact) strongly compact cardinals. We then show, relative to the existence of a non-trivial (proper or improper) class of supercompact cardinals, that it is possible to have a model with the same class of supercompact cardinals in which every measurable cardinal δ is $2^{δ}$ strongly compact.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 167
• Numer: 1
• Strony: 65-78

Daty

wydano

2001

Twórcy

autor

Arthur W. Apter

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

Identyfikatory

DOI

10.4064/fm167-1-5