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