Omitted type

A type $p(x_1,\dots ,x_n)$ is omitted in a structure $M$ when no tuple from $M^n$ realizes every formula in $p$.

Let $T$ be a consistent theory in a countable first-order language. For every countable family of nonisolated finite-arity types of $T$, there is a countable model of $T$ that omits every type in the family.