Model companions of theories with an automorphism

Abstract

For a theory $T$ in $L,T_{\sigma }$ is the theory of the models of $T$ with an automorphism $\sigma$. If $T$ is an unstable model complete theory without the independence property, then $T_{\sigma }$ has no model companion. If $T$ is an unstable model complete theory and $T_{\sigma }$ has the amalgamation property, then $T_{\sigma }$ has no model companion. If $T$ is model complete and has the fcp, then $T_{\sigma }$ has no model completion.