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## Fundamenta Mathematicae

2007 | 194 | 3 | 253-265
Tytuł artykułu

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

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EN
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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.
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Tom
Numer
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253-265
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wydano
2007
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autor
• 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.
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