First order rigidity of non-uniform higher rank arithmetic lattices

Abstract

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

Preliminary version. Comments are welcome