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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2511.22742 |
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| _version_ | 1866912734846648320 |
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| author | Piepenborn, Ricardo Palomino |
| author_facet | Piepenborn, Ricardo Palomino |
| contents | It is shown that images of cross-sections of surjective morphisms $f: Γ\longrightarrow Δ$ of divisible abelian $o$-groups are exactly divisible, tame (equivalently, relative Dedekind complete) and cofinal subgroups of $Γ$ compatible with $f$ in a suitable sense. The note concludes with an application to real closed valued fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cross-Sections of Divisible Abelian $o$-Groups via Tame Pairs Piepenborn, Ricardo Palomino Logic 06F20, 03C64, 12J15 It is shown that images of cross-sections of surjective morphisms $f: Γ\longrightarrow Δ$ of divisible abelian $o$-groups are exactly divisible, tame (equivalently, relative Dedekind complete) and cofinal subgroups of $Γ$ compatible with $f$ in a suitable sense. The note concludes with an application to real closed valued fields. |
| title | Cross-Sections of Divisible Abelian $o$-Groups via Tame Pairs |
| topic | Logic 06F20, 03C64, 12J15 |
| url | https://arxiv.org/abs/2511.22742 |