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

2025/11/27 by Piepenborn, Ricardo Palomino
#03C64 #06F20 #12J15 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2511.22742

Abstract

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.

Related

• The Structure of Divisible Abelian Groups
• Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields
• Cuts and small extensions of abelian ordered groups
• Tame coverings of arithmetic schemes
• Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order