Definition:Finite Character

Definition
Let $S$ be a set.

Let $\mathcal F$ be a set of subsets of $S$.

Then $\mathcal F$ has finite character iff for each $A \subseteq S$:


 * $A \in \mathcal F$ iff every finite subset of $A$ is in $\mathcal F$.

Also see

 * Tukey-Teichmüller Theorem / Tukey's Lemma, an equivalent of the Axiom of Choice
 * Restricted Tukey-Teichmüller Theorem, an equivalent of the Boolean Prime Ideal Theorem.