The aim of this paper is to generalize and improve two of the main model-theoretic results of “Stable group theory and approximate subgroups” by Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence of Lie models. The second one is the Stabilizer Theorem. In the process, a systematic study of the structure of piecewise hyperdefinable sets is developed. In particular, we show the most significant properties of their logic topologies.

中文翻译：

---

关于分段超定义群

本文的目的是将 Hrushovski 的“稳定群论和近似子群”的两个主要模型理论成果推广和改进到分段超定义集的背景下。第一个是李模型的存在。第二个是稳定定理。在此过程中，对分段超定义集的结构进行了系统研究。特别是，我们展示了它们的逻辑拓扑的最重要的属性。