English

A small ultrafilter number at smaller cardinals

Logic 2019-04-05 v1

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 ω+1{\aleph}_{\omega+1} which is generated by fewer than 2ω+1{2}^{{\aleph}_{\omega+1}} sets.

Keywords

Cite

@article{arxiv.1904.02379,
  title  = {A small ultrafilter number at smaller cardinals},
  author = {Dilip Raghavan and Saharon Shelah},
  journal= {arXiv preprint arXiv:1904.02379},
  year   = {2019}
}

Comments

8 pages. Submitted