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 $M$ if and only if, for every finite subset $P \subseteq S$:

$f {\restriction_P} \in M$

where $f {\restriction_P}$ denotes the restriction of $f$ to $P$.

Sources

• 1973: Thomas J. Jech: The Axiom of Choice: $2.3$ The Prime Ideal Theorem