Omitting Types Theorem

Theorem
Let $\mathcal{L}$ be a countable language.

Let $T$ be an $\mathcal{L}$-theory.

Let $\{p_i : i \in \mathbb N \}$ be a countable set of non-isolated $n$-types of $T$.

There is a countable $\mathcal{L}$-structure $\mathcal{M}$ such that $\mathcal{M}\models T$ and $\mathcal{M}$ omits each $p_i$.