Eventual extensions of finite codes

Abstract

Suppose S S and T T are shift equivalent mixing shifts of finite type, and f f is a conjugacy from a subsystem of S S to a subsystem of T T . Then for any sufficiently large n n , f f extends to a conjugacy of S n {S^n} and T n {T^n} . A consequence of the proof is a fortified version of Wagoner’s Stable FOG Theorem.