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arXiv · 2010.07970

Is being a higher rank lattice a first order property?

Nir Avni·Chen Meiri
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Abstract

We show that there is a sentence $\varphi$ in the first order language of groups such that a finitely generated group $\Gamma$ satisfies $\varphi$ if and only if $\Gamma$ is isomorphic to a group of the form $\mathrm{PSL}_n(O)$, where $n \geq 3$ and $O$ is a ring of $S$-integers in a number field.

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Nir Avni, Chen Meiri. 2020-10-15. Is being a higher rank lattice a first order property?. https://arxiv.org/abs/2010.07970

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