We prove the following algebraic characterization of elementary equivalence: $\equiv$ restricted to countable structures of finite type is minimal among the equivalence relations, other than isomorphism, which are preserved under reduct and renaming and which have the Robinson property; the latter is a faithful adaptation for equivalence relations of the familiar model theoretical notion. We apply this result to Friedman's fourth problem by proving that if $L = L_{\omega\omega}(Q^i)_{i \in \omega_1}$ is an $(\omega_1, \omega)$-compact logic satisfying both the Robinson consistency theorem on countable structures of finite type and the Lowenheim-Skolem theorem for some $\lambda < \omega_\omega$ for theories having $\omega_1$ many sentences, then $\equiv_L = \equiv$ on such structures.