Variations of cub filter on 𝒫_{𝜅}𝜆

Matsubara, Yo

doi:10.1090/S0002-9939-1988-0934884-X

Variations of cub filter on $\mathcal {P}_ \kappa \lambda$
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by Yo Matsubara

Proc. Amer. Math. Soc. 102 (1988), 1009-1017

DOI: https://doi.org/10.1090/S0002-9939-1988-0934884-X

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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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