Closure sets of functions and a hierarchy of filters
HTML articles powered by AMS MathViewer
- by Robert Mignone PDF
- Proc. Amer. Math. Soc. 114 (1992), 799-807 Request permission
Abstract:
This paper presents a transfinite extension of a filter generating closure property of functions. One consequence of this extension is a hierarchy of filters which coincide with filters generated by a directed set type closure property. At each level of this hierarchy a progressively stronger notion of normality is satisfied. Ideals with this stronger notion of normality each have a corresponding saturation characterization.References
- James E. Baumgartner, Alan D. Taylor, and Stanley Wagon, On splitting stationary subsets of large cardinals, J. Symbolic Logic 42 (1977), no. 2, 203–214. MR 505505, DOI 10.2307/2272121
- 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 T. J. Jech, Set theory, Academic Press, 1978.
- 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
- C. A. Johnson, On saturated ideals and $P_\kappa \lambda$, Fund. Math. 129 (1988), no. 3, 215–221. MR 962544, DOI 10.4064/fm-129-3-215-221
- 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
- Yo Matsubara, Splitting $P_\kappa \lambda$ into stationary subsets, J. Symbolic Logic 53 (1988), no. 2, 385–389. MR 947845, DOI 10.2307/2274510
- 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
- Robert Mignone, A direct weakening of normality for filters, Rocky Mountain J. Math. 22 (1992), no. 4, 1447–1458. MR 1201103, DOI 10.1216/rmjm/1181072666
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 799-807
- MSC: Primary 03E05
- DOI: https://doi.org/10.1090/S0002-9939-1992-1070526-4
- MathSciNet review: 1070526