We present upper and lower bounds on the per-user multiplexing gain (MG) of Wyner's circular soft-handoff model and Wyner's circular full model with cognitive transmitters and receivers with cache memories. The bounds are tight for cache memories with prelog $μ\geq 2/3D$ in the soft-handoff model and for $μ\geq D$ in the full model, where $D$ denotes the number of possibly demanded files. In these cases the per-user MG of the two models is $1+μ/D$, the same as for non-interfering point-to-point links with caches at the receivers. Large receiver cache-memories thus allow to completely mitigate interference in these networks.