English

$\widetilde{\mid}\hspace{1mm}$-divisibility of ultrafilters

Logic 2017-03-20 v1

Abstract

We further investigate a divisibility relation on the set βN\beta N of ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

Keywords

Cite

@article{arxiv.1703.05999,
  title  = {$\widetilde{\mid}\hspace{1mm}$-divisibility of ultrafilters},
  author = {Boris Šobot},
  journal= {arXiv preprint arXiv:1703.05999},
  year   = {2017}
}