There may be no nowhere dense ultrafilter
Abstract
We show the consistency of ZFC +''there is no NWDultrafilter 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
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1996
 DOI:
 10.48550/arXiv.math/9611221
 arXiv:
 arXiv:math/9611221
 Bibcode:
 1996math.....11221S
 Keywords:

 Mathematics  Logic
 EPrint:
 Lecture Notes Logic 11 (1998), 305324