There may be no nowhere dense ultrafilter
Logic
2009-09-25 v1
Abstract
We show the consistency of ZFC +''there is no NWD-ultrafilter on omega'', which means: for every non principle ultrafilter D on the set of natural numbers, there is a function f from the set of natural numbers to the reals, such that for some nowhere dense set A of reals, the set {n: f(n) in A} is not in D. This answers a question of van Douwen, which was put in more general context by Baumgartner
Keywords
Cite
@article{arxiv.math/9611221,
title = {There may be no nowhere dense ultrafilter},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9611221},
year = {2009}
}