On piecewise hyperdefinable groups

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.

Automated summary

The aim of this paper is to extend and improve two of the main model-theoretic results by Hrushovski in the context of piecewise hyperdefinable sets, namely the existence of Lie models and the Stabilizer Theorem. This study also includes a systematic investigation of the structure of piecewise hyperdefinable sets, particularly focusing on their logic topologies.