Level by level equivalence and the number of normal measures over $P_{κ}(λ)$

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

Abstrakty

EN

We construct two models for the level by level equivalence between strong compactness and supercompactness in which if κ is λ supercompact and λ ≥ κ is regular, we are able to determine exactly the number of normal measures $P_{κ}(λ)$ carries. In the first of these models, $P_{κ}(λ)$ carries $2^{2^{[λ]^{<κ}}}$ many normal measures, the maximal number. In the second of these models, $P_{κ}(λ)$ carries $2^{2^{[λ]^{<κ}}}$ many normal measures, except if κ is a measurable cardinal which is not a limit of measurable cardinals. In this case, κ (and hence also $P_{κ}(κ)$) carries only κ⁺ many normal measures. In both of these models, there are no restrictions on the structure of the class of supercompact cardinals.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 194
• Numer: 3
• Strony: 253-265

Daty

wydano

2007

Twórcy

autor

Arthur W. Apter

• Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.
• The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, NY 10016, U.S.A.

Identyfikatory

DOI

10.4064/fm194-3-3