Definition:Binary Mess/Consistent Mapping

Definition
Let $S$ be a set.

Let $M$ be a binary mess on $S$.

Let $f : S \to \Bbb B$ be a mapping from $S$ to a Boolean domain.

Then, $f$ is consistent with $M$, for every finite subset $P \subseteq S$:
 * $f \restriction_P \in M$

where $f \restriction_P$ is the restriction of $f$ to $P$.