2 problems

Let $T$ be a model-complete theory with infinite models, and let $T^*_{\operatorname{Aut}}$ denote the model companion, if it exists, of the theory obtained by expanding models of…

Let $T$ be a complete theory, and let $T^*$ be a model-complete expansion of $T$ by definitions. Let $T_{\sigma}$ be the theory obtained by adding a unary function symbol $\sigma$…