On the model theory of higher rank arithmetic groups

2020/08/04 by Nir Avni, Avni, Nir, Chen Meiri +1 · 3 citations
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2008.01793

Abstract

Let Γ be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if Γ is either non-uniform or is uniform of orthogonal type and dimension at least 9, then Γ is bi-interpretable with the ring ℤ of integers. It follows that the first order theory of Γ is undecidable, that all finitely generated subgroups of Γ are definable, and that Γ is characterized by a single first order sentence among all finitely generated groups.

Cited by

• Elementary equivalence of Kac-Moody groups
• Is being a higher rank lattice a first order property?
• On first order rigidity for linear groups

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