\begin{definition}[Definition:Model (Predicate Logic)]
Let $\LL_1$ be the language of predicate logic.
Let $\AA$ be a structure for predicate logic.
Then $\AA$ '''models''' a sentence $\mathbf A$ {{iff}}:
:$\map {\operatorname{val}_\AA} {\mathbf A} = T$
where $\map {\operatorname{val}_\AA} {\mathbf A}$ denotes the value of $\mathbf A$ in $\AA$.
This relationship is denoted:
:$\AA \models_{\mathrm{PL} } \mathbf A$
When pertaining to a collection of sentences $\FF$, one says $\AA$ '''models''' $\FF$ {{iff}}:
:$\forall \mathbf A \in \FF: \AA \models_{\mathrm{PL} } \mathbf A$
that is, {{iff}} it '''models''' all elements of $\FF$.
This can be expressed symbolically as:
:$\AA \models_{\mathrm {PL} } \FF$
\end{definition}