Definition:Isolated Type

Definition

Let $T$ be an $\LL$-theory.

Let $\map \phi {\bar v}$ be an $\LL$-formula in $n$ free variables $\bar v$ such that $T \cup \map \phi {\bar v}$ is satisfiable.

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

We say that $\phi$ isolates $p$ if and only if for all $\psi \in p$, we have:

$T \models \forall \map {\bar v} {\map \phi {\bar v} \rightarrow \map \psi {\bar v} }$

that is, all $\psi$ are semantic consequences of $\phi$.

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