Definition:Finite Character

Definition
Let $S$ be a set.

Let $\mathcal A$ be a set of finite subsets of $S$.

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


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

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.