Definition 13.2 ($n$-type). Let $M$ be an $L$-structure and $A\subseteq M$. An $n$-type over $A$ with respect to $M$ is a set of $L$-formulas with parameters from $A$, in free variables $x_1,\dots ,x_n$ such that $p\cup {Th}_A(M)$ is consistent.

An $n$-type is complete if for every $L_A$-formula with $n$ variables $\varphi$, either $\varphi \in p$ or $\neg \varphi \in p$.

Let $S_n^M(A)$ denote the set of all complete $n$-types over $A$ with respect to $M$.