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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 (2,0)(2, {\aleph}_{0})-selective ultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved that the existence of (2,0)(2, {\aleph}_{0})-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