Definition:Binary Mess

Definition
Let $S$ be a set.

Let $I$ be the set of all finite subsets of $S$.

Let $\Bbb B$ be a Boolean domain.

Let $M$ be a set defined as:
 * $\ds M \subseteq \bigcup_{P \mathop \in I} \Bbb B^P$

where $\Bbb B^P$ denotes the set of all mappings from $P$ to $\Bbb B$.

That is, such that $M$ is a set of mappings from finite subsets of $S$ to $\Bbb B$.

Suppose that $M$ satisfies the binary mess axioms:

Then $M$ is a binary mess on $S$.