AI 中文总结
该研究在有序阿贝尔群纯语言中肯定解答Kourovka笔记问题18.16，通过代数刚性定理得出相关结论，且无参数纯语言情形适用，扩张语言变体存在反例。
AI 中文摘要
我们在允许参数的有序阿贝尔群纯语言中肯定地解答了《Kourovka笔记》问题18.16。可定义函数的分段仿射描述将问题简化为一个代数刚性定理：由有限个有理仿射法则覆盖的无挠阿贝尔群的加性自同态具有全局有理斜率。该结果包含无参数的纯语言情形，而无限制的扩张语言变体存在一个简单反例。
英文摘要
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.
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