Definition:Isolated Type
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The term Definition:Logical Formula as used here has been identified as being ambiguous.
If you are familiar with this area of mathematics, you may be able to help improve $\mathsf{Pr} \infty \mathsf{fWiki}$ by determining the precise term which is to be used.
Definition
Let $T$ be an $\mathcal L$-theory.
Let $\phi \left({\bar v}\right)$ be an $\mathcal L$-formula in $n$ free variables $\bar v$ such that $T \cup \phi \left({\bar v}\right)$ is satisfiable.
If you are familiar with this area of mathematics, you may be able to help improve $\mathsf{Pr} \infty \mathsf{fWiki}$ by determining the precise term which is to be used.
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Let $p$ be an $n$-type of $T$.
We say that $\phi$ isolates $p$ if for all $\psi \in p$, we have:
- $T \models \forall \bar{v} \left({ \phi \left({\bar v}\right) \rightarrow \psi \left({\bar v}\right) }\right)$
that is, all $\psi$ are semantic consequences of $\phi$.
