Definition:Finite Character/Mappings

Definition
Let $S$ and $T$ be sets.

Let $\mathcal F$ be a set of mappings from subsets of $S$ to $T$.

That is, let $\mathcal F$ be a set of partial mappings from $S$ to $T$.

Then $\mathcal F$ has finite character iff for each partial mapping $f \subseteq S \times T$:


 * $f \in \mathcal F$ iff for each finite subset $K$ of the domain of $f$, the restriction of $f$ to $K$ is in $\mathcal F$.

Also see

 * Finite Character for Sets of Mappings
 * Cowen-Engeler Lemma, an equivalent of the Boolean Prime Ideal Theorem.