= Solution
Suppose $a\notin\operatorname{acl}(A)$. Choose a small model $M_0$ containing $A$. The <complete type> $\operatorname{tp}(a/A)$ is nonalgebraic, so choose a realization $a'\notin M_0$. Strong homogeneity of the <monster model> gives an automorphism $\sigma$ fixing $A$ with $\sigma(a)=a'$. Then $M=\sigma^{-1}(M_0)$ contains $A$, but $a\in M$ would imply $a'=\sigma(a)\in M_0$. Taking the contrapositive proves
$$
\boxed{a\in M\text{ for every model }M\supseteq A\Longrightarrow a\in\operatorname{acl}(A).}
$$
Back to article page
