One-point extension between atomic models
= One-point extension between atomic models
If $M,N$ are infinite atomic models of a complete theory and a finite partial elementary map sends $\bar a$ to $\bar b$, then for every $c\in M$ there is $d\in N$ extending it by $c\mapsto d$. An isolating formula for $\operatorname{tp}(\bar a,c)$ supplies $d$. Back-and-forth therefore makes any two countable atomic models isomorphic.