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arXiv · 2511.22742

Cross-Sections of Divisible Abelian $o$-Groups via Tame Pairs

Ricardo Palomino Piepenborn
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Abstract

It is shown that images of cross-sections of surjective morphisms $f: \Gamma \longrightarrow \Delta$ of divisible abelian $o$-groups are exactly divisible, tame (equivalently, relative Dedekind complete) and cofinal subgroups of $\Gamma$ compatible with $f$ in a suitable sense. The note concludes with an application to real closed valued fields.

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Ricardo Palomino Piepenborn. 2025-11-27. Cross-Sections of Divisible Abelian $o$-Groups via Tame Pairs. https://arxiv.org/abs/2511.22742

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