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A Cardinal Structure Theorem for an Ultrapower

Published online by Cambridge University Press:  20 November 2018

Arthur W. Apter
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Abstract

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In this note, we construct a model with a normal measure U over a measurable cardinal κ so that the cardinal structures of V and Vκ/U are the same ≤2κ. We then show that it is possible to construct a model where this is not true.

Keywords

03C20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 4 , 01 December 1985 , pp. 472 - 473
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Laver, R., Making the Supercompactness of ĸ Indestructible under ĸ-Directed Closed Forcing, Israel J. Math. 29(4), (1978) pp. 385–388.Google Scholar
2. Menas, T.K., On Strong Compactness and Supercompactness, Annals of Math. Logic, 7, (1975), pp. 327–359.Google Scholar