Open Colorings and Baumgartner's Axiom
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914232831836160 |
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| author | Notaro, Lorenzo |
| author_facet | Notaro, Lorenzo |
| contents | We construct a model of $\mathsf{MA_{\aleph_1}}+\mathsf{OCA}_T$ where Baumgartner's Axiom fails, settling a question of Farah. Moreover, in the same model there is an $\aleph_1$-dense set of reals which is neither reversible nor increasing, answering a question of Marun, Shelah, and Switzer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01166 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Open Colorings and Baumgartner's Axiom Notaro, Lorenzo Logic 03E35 (Primary) 03E05, 03E50 (Secondary) We construct a model of $\mathsf{MA_{\aleph_1}}+\mathsf{OCA}_T$ where Baumgartner's Axiom fails, settling a question of Farah. Moreover, in the same model there is an $\aleph_1$-dense set of reals which is neither reversible nor increasing, answering a question of Marun, Shelah, and Switzer. |
| title | Open Colorings and Baumgartner's Axiom |
| topic | Logic 03E35 (Primary) 03E05, 03E50 (Secondary) |
| url | https://arxiv.org/abs/2601.01166 |