First order rigidity of high-rank arithmetic groups

The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics. It includes $\mathrm{SL}(n,\mathbb{Z})$, for $n>2$ , $\mathrm{SL}(n, \mathbb{Z}[1/p])$ for $n>1$, their finite index subgroups and many more. A number of remarkable results about them have been proven including; Weil local rigidity, Mostow strong rigidity, Margulis Super rigidity and the Schwartz-Eskin-Farb Quasi-isometric rigidity.
We will add a new type of rigidity : "first order rigidity". Namely if $D$ is such a non-uniform characteristic zero arithmetic group and L a finitely generated group which is elementary equivalent to $D$ then $L$ is isomorphic to $D$.
This stands in contrast with Zlil Sela's remarkable work which implies that the free groups, surface groups and hyperbolic groups (many of which are low-rank arithmetic groups) have many non isomorphic finitely generated groups which are elementary equivalent to them.
Based on a joint paper with Nir Avni and Chen Meiri (Invent. Math. 217(2019) 219-240).