Definition:Forking Extension

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

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

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

Let $p(\bar x)$ 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 non-forking extension of $p\restriction A$ if $p(\bar x)$ does not fork over $A$.