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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Variations of cub filter on $ \mathcal{P}\sb \kappa\lambda$


Author: Yo Matsubara
Journal: Proc. Amer. Math. Soc. 102 (1988), 1009-1017
MSC: Primary 03E05; Secondary 03E55, 03E60, 04A20
MathSciNet review: 934884
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Abstract: In his 1973 paper, Jech extended the notion of cub and stationary sets to such sets in $ {\mathcal{P}_\kappa }\lambda $ and showed that many of their properties are preserved. We study variations of cub filters in this paper. We make use of the partition property (a large cardinal hypothesis) to investigate the properties of these filters. In the last section we investigate the relation of our filter to supercompact filters on $ {\mathcal{P}_{{\aleph _1}}}\lambda $ under the Axiom of Determinacy. This motivates the formulation of a certain infinitary partition property, and this property implies the $ \lambda $-supercompactness of $ {\aleph _1}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934884-X
PII: S 0002-9939(1988)0934884-X
Article copyright: © Copyright 1988 American Mathematical Society