2 problems

Let $T$ be a first-order countable unstable theory. Two models $M$ and $N$ of $T$ are random twins if they are non-isomorphic but become isomorphic after the universe is extended b…

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…