Year: 2026
Type: preprint
Abstract: We answer Kourovka Notebook Problem~18.16 affirmatively in the pure language of ordered abelian groups, with parameters allowed. The piecewise-affine description of definable functions reduces the question to an algebraic rigidity theorem: an additive endomorphism of a torsion-free abelian group that is covered by finitely many rational-affine laws has one global rational slope. The parameter-free pure-language case is included, whereas the unrestricted expansion-language variant admits a simple counterexample.
Source: arXiv (Cornell University)
Authors: Ji, Haitao, Xu, Fengshuo, Qiu, Dong
Institution: Guangxi University
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2923803343
OpenAlex ID: W7203777330
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