Nontrivial automorphisms of $\mathcal P(ω)/\mathrm{Fin}$ in Cohen models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908871646248960 |
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| author | Brian, Will Dow, Alan |
| author_facet | Brian, Will Dow, Alan |
| contents | We show that if $κ< \aleph_ω$ Cohen reals are added to a model of $\mathsf{CH}$, then there are nontrivial automorphisms of $\mathcal P(ω)/\mathrm{Fin}$ in the extension. Under some further hypotheses on the ground model, namely the existence of long enough sage Davies trees (which follows from $\mathsf{SCH}$ plus $\square_λ$ for every $λ$ with $\mathrm{cf}(λ) = ω$), we prove the same result for cardinals $κ\geq \aleph_ω$ as well. This extends a result a Shelah and Steprāns, who proved the result for $κ= \aleph_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07214 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nontrivial automorphisms of $\mathcal P(ω)/\mathrm{Fin}$ in Cohen models Brian, Will Dow, Alan Logic General Topology We show that if $κ< \aleph_ω$ Cohen reals are added to a model of $\mathsf{CH}$, then there are nontrivial automorphisms of $\mathcal P(ω)/\mathrm{Fin}$ in the extension. Under some further hypotheses on the ground model, namely the existence of long enough sage Davies trees (which follows from $\mathsf{SCH}$ plus $\square_λ$ for every $λ$ with $\mathrm{cf}(λ) = ω$), we prove the same result for cardinals $κ\geq \aleph_ω$ as well. This extends a result a Shelah and Steprāns, who proved the result for $κ= \aleph_2$. |
| title | Nontrivial automorphisms of $\mathcal P(ω)/\mathrm{Fin}$ in Cohen models |
| topic | Logic General Topology |
| url | https://arxiv.org/abs/2603.07214 |