Axiom:Filter on Set Axioms

Definition
Let $S$ be a set.

Let $\powerset S$ denote the power set of $S$.

Let $\FF \subset \powerset S$.

Axioms 1
$\FF$ is said to satisfy the filter on set axioms  $\FF$ satisfies the following axioms:

Axioms 2
$\FF$ is said to satisfy the filter on set axioms  $\FF$ satisfies the following axioms:

Also see

 * Definition:Filter on Set