Is being a higher rank lattice a first order property?

2020/10/15 by Nir Avni, Avni, Nir, Chen Meiri +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2010.07970

openalex publication_date 2020/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there is a sentence φ in the first order language of groups such that a finitely generated group Γ satisfies φ if and only if Γ is isomorphic to a group of the form PSL_n(O), where n ≥ 3 and O is a ring of S-integers in a number field.

Citations

• On the model theory of higher rank arithmetic groups

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