Weakly normal filters and the closed unbounded filter on 𝑃_{𝜅}𝜆

Abe, Yoshihiro

doi:10.1090/S0002-9939-1988-0935101-7

Weakly normal filters and the closed unbounded filter on $P_ \kappa \lambda$
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by Yoshihiro Abe

Proc. Amer. Math. Soc. 104 (1988), 1226-1234

DOI: https://doi.org/10.1090/S0002-9939-1988-0935101-7

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Abstract:

Assuming that $\kappa$ is supercompact and $\lambda$ is inaccessible, we present two isomorphic fine measures on ${P_\kappa }\lambda$ containing the closed unbounded filter. Some remarks on the (strongly) closed unbounded filter and weakly normal filters are added.

References

Yoshihiro Abe, Some results concerning strongly compact cardinals, J. Symbolic Logic 50 (1985), no. 4, 874–880 (1986). MR 820119, DOI 10.2307/2273977
Donna M. Carr, The minimal normal filter on $P_{\kappa }\lambda$, Proc. Amer. Math. Soc. 86 (1982), no. 2, 316–320. MR 667297, DOI 10.1090/S0002-9939-1982-0667297-3
Moti Gitik, Nonsplitting subset of ${\scr P}_\kappa (\kappa ^+)$, J. Symbolic Logic 50 (1985), no. 4, 881–894 (1986). MR 820120, DOI 10.2307/2273978
Thomas J. Jech, Some combinatorial problems concerning uncountable cardinals, Ann. Math. Logic 5 (1972/73), 165–198. MR 325397, DOI 10.1016/0003-4843(73)90014-4
Jussi Ketonen, Ultrafilters over measurable cardinals, Fund. Math. 77 (1973), no. 3, 257–269. MR 329897, DOI 10.4064/fm-77-3-257-269
A. Kanamori, Weakly normal filters and irregular ultrafilters, Trans. Amer. Math. Soc. 220 (1976), 393–399. MR 480041, DOI 10.1090/S0002-9947-1976-0480041-X
Telis K. Menas, On strong compactness and supercompactness, Ann. Math. Logic 7 (1974/75), 327–359. MR 357121, DOI 10.1016/0003-4843(75)90009-1
Telis K. Menas, A combinatorial property of $p_{k}\lambda$, J. Symbolic Logic 41 (1976), no. 1, 225–234. MR 409186, DOI 10.2307/2272962
Robert M. Solovay, William N. Reinhardt, and Akihiro Kanamori, Strong axioms of infinity and elementary embeddings, Ann. Math. Logic 13 (1978), no. 1, 73–116. MR 482431, DOI 10.1016/0003-4843(78)90031-1