Archive for Mathematical Logic 59 (3-4):325-334 (2020)

Abstract
It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on \ which is generated by fewer than \ sets.
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DOI 10.1007/s00153-019-00693-8
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References found in this work BETA

Iterated Perfect-Set Forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
The Weak □* is Really Weaker Than the Full □.Shai Ben-David & Menachem Magidor - 1986 - Journal of Symbolic Logic 51 (4):1029 - 1033.
Iterated Perfectset Forcing.J. E. Baumgartner - 1979 - Annals of Mathematical Logic 17 (3):271.

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