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arXiv · 1709.02766

First order rigidity of non-uniform higher rank arithmetic lattices

Nir Avni·Alexander Lubotzky·Chen Meiri
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Abstract

If $\Gamma$ is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example, $SL_n(\mathbb{Z})$, $n \geq 3$) and $\Lambda$ is a finitely generated group that is elementarily equivalent to $\Gamma$, then $\Lambda$ is isomorphic to $\Gamma$.

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Nir Avni, Alexander Lubotzky, Chen Meiri. 2017-09-08. First order rigidity of non-uniform higher rank arithmetic lattices. https://arxiv.org/abs/1709.02766

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