Definition:Isolated Type

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

Let $\phi(\bar{v})$ be an $\mathcal{L}$-formula in $n$-free variables such that $T \cup \phi(\bar{v})$ is satisfiable.

Let $p$ be an $n$-type of $T$.

We say that $\phi$ isolates $p$ if for all $\psi \in p$, we have $T\models \forall \bar{v} \left( \phi(\bar v) \rightarrow \psi(\bar v)\right)$.