Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters
Logic
2024-08-21 v1
Abstract
We exhibit a forcing for producing a model with no nowhere dense ultrafilters that satisfies the full Sacks Property. By interleaving this forcing with other forcing notions, a model containing a -selective ultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved that the existence of -selective ultrafilters does not imply the existence of nowhere dense ultrafilters.
Keywords
Cite
@article{arxiv.2408.04446,
title = {Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters},
author = {Dilip Raghavan and Juris Steprāns},
journal= {arXiv preprint arXiv:2408.04446},
year = {2024}
}
Comments
17 Pages, Submitted