Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913473054638080 |
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| author | Raghavan, Dilip Steprāns, Juris |
| author_facet | Raghavan, Dilip Steprāns, Juris |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters Raghavan, Dilip Steprāns, Juris Logic 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. |
| title | Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters |
| topic | Logic |
| url | https://arxiv.org/abs/2408.04446 |