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arXiv · 2408.04446

Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters

Dilip Raghavan·Juris Steprāns
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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 $(2, {\aleph}_{0})$-selective ultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved that the existence of $(2, {\aleph}_{0})$-selective ultrafilters does not imply the existence of nowhere dense ultrafilters.

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Dilip Raghavan, Juris Steprāns. 2024-08-08. Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters. https://arxiv.org/abs/2408.04446

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