Definable equivalence relations and zeta functions of groups

Ehud Hrushovski, Ben Martin, Silvain Rideau +1

We prove that the theory of the $p$-adics ${\mathbb{Q}}_p$ admits elimination of imaginaries provided we add a sort for ${\mathrm{GL}}_n({\mathbb{Q}}_p)/{\mathrm{GL}}_n({\mathbb{Z}}_p)$ for eac…