A filter on [𝜆]^{𝜅}

Di Prisco, C. A.; Marek, W.

doi:10.1090/S0002-9939-1984-0733412-8

A filter on $[\lambda ]^{\kappa }$
HTML articles powered by AMS MathViewer

by C. A. Di Prisco and W. Marek

Proc. Amer. Math. Soc. 90 (1984), 591-598

DOI: https://doi.org/10.1090/S0002-9939-1984-0733412-8

PDF | Request permission

Abstract:

We define a filter on ${\left [ \lambda \right ]^\kappa }$ with properties similar to those of the closed unbounded filter in ${P_\kappa }\left ( \lambda \right )$. This filter’s behaviour depends on set theoretical hypotheses.

References

Many-times huge and multihuge cardinals

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
C. A. Di Prisco and W. Marek, Some properties of stationary sets, Dissertationes Math. (Rozprawy Mat.) 218 (1983), 37. MR 722012
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
Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
M. Magidor, Combinatorial characterization of supercompact cardinals, Proc. Amer. Math. Soc. 42 (1974), 279–285. MR 327518, DOI 10.1090/S0002-9939-1974-0327518-9
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 J. Mignone, The ultrafilter characterization of huge cardinals, Proc. Amer. Math. Soc. 90 (1984), no. 4, 585–590. MR 733411, DOI 10.1090/S0002-9939-1984-0733411-6
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