Definition:Forking Extension

Definition
Let $T$ be a complete $\LL$-theory.

Let $\mathfrak C$ be a monster model for $T$.

Let $A\subseteq B$ be subsets of the universe of $\mathfrak C$.

Let $\map p {\bar x}$ be a complete $n$-type over $B$.

Denote by $p \restriction A$ the subset of $p$ consisting of those formulas which involve only parameters from $A$.

$p$ is a forking extension of $p \restriction A$ $\map p {\bar x}$ forks over $A$.