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 \({\aleph }_{\omega +1}\) which is generated by fewer than \({2}^{{\aleph }_{\omega +1}}\) sets.
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First author was partially supported by the Singapore Ministry of Education’s research Grant Number MOE2017-T2-2-125.
Both authors were partially supported by European Research Council Grant 338821. Publication 1160 on Shelah’s list.
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Raghavan, D., Shelah, S. A small ultrafilter number at smaller cardinals. Arch. Math. Logic 59, 325–334 (2020). https://doi.org/10.1007/s00153-019-00693-8
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DOI: https://doi.org/10.1007/s00153-019-00693-8