A small ultrafilter number at smaller cardinals

Archive for Mathematical Logic:1-10 (forthcoming)

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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