AI 中文总结
该研究针对非初等无扭双曲群建立一致小消去定理，并将其应用于证明这类群的一阶理论不具有模型伴侣。
AI 中文摘要
我们针对非初等无扭双曲群建立了一致小消去定理：给定任意预设的小消去常数，有限个固定单词足以从每对非交换元素中生成一个小消去元素。作为应用，我们证明每个非初等无扭双曲群的一阶理论都不具有模型伴侣。
英文摘要
We establish a uniform small cancellation theorem for non-elementary torsion-free hyperbolic groups: given any prescribed small cancellation constant, finitely many fixed words suffice to produce a small cancellation element from every pair of noncommuting elements. As an application, we prove that the first-order theory of every non-elementary torsion-free hyperbolic group does not admit a model companion.
