\begin{definition}[Definition:Finite Character/Mappings]
Let $S$ and $T$ be sets.
Let $\FF$ be a set of mappings from subsets of $S$ to $T$.
That is, let $\FF$ be a set of partial mappings from $S$ to $T$.
Then $\FF$ has '''finite character''' {{iff}} for each partial mapping $f \subseteq S \times T$:
:$f \in \FF$ {{iff}} for each finite subset $K$ of the domain of $f$, the restriction of $f$ to $K$ is in $\FF$.
\end{definition}