On piecewise hyperdefinable groups

2020/11/23 by Arturo Rodriguez Fanlo, Fanlo, Arturo Rodriguez · 2 citations
Mathematics · #03C45 #03C68 #11P70 #20A15 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · doi:10.48550/arxiv.2011.11669

openalex publication_date 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 E. 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.

Cited by

• Model theory of difference fields with an additive character on the fixed field
• A short note on the Massicot-Wagner method

Related

• Stable group theory and approximate subgroups
• Hyperdefinability of the Lie model for approximate subgroups
• Model theory of finite and pseudofinite groups
• Hyperlinear approximations to amenable groups come from sofic approximations
• Cantor systems, piecewise translations and simple amenable groups