A lattice in a Lie group is a discrete subgroup of finite co-volume. In many contexts, lattices in Lie groups of rank one (such as SL(2,R)) behave differently from lattices in higher-rank Lie groups (suchas SL(n,R), for n>2). Such phenomenon is usually called rigidity. I will talk about a manifestation of this dichotomy in Model Theory. The main result is that many higher-rank lattices (and conjecturally, all of them) are bi-interpretable with the integers.

Based on joint works with Alex Lubotzky and Chen Meiri.