# Sh:594

- Shelah, S. (1998).
*There may be no nowhere dense ultrafilter*. In Logic Colloquium ’95 (Haifa), Vol. 11, Springer, Berlin, pp. 305–324. arXiv: math/9611221 DOI: 10.1007/978-3-662-22108-2_17 MR: 1690694 -
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 - published version (12p)

Bib entry

@incollection{Sh:594, author = {Shelah, Saharon}, title = {{There may be no nowhere dense ultrafilter}}, booktitle = {{Logic Colloquium '95 (Haifa)}}, series = {Lecture Notes Logic}, volume = {11}, year = {1998}, pages = {305--324}, doi = {10.1007/978-3-662-22108-2_17}, mrclass = {03E05 (03E35)}, mrnumber = {1690694}, doi = {10.1007/978-3-662-22108-2_17}, publisher = {Springer, Berlin}, note = {\href{https://arxiv.org/abs/math/9611221}{arXiv: math/9611221}}, arxiv_number = {math/9611221} }