Definition:Comparable Filters on Set

Definition
Let $S$ be a set.

Let $\mathcal P \left({S}\right)$ be the power set of $S$.

Let $\mathcal F, \mathcal F' \subset \mathcal P \left({S}\right)$ be two filters on $S$.

$\mathcal F$ and $\mathcal F'$ are comparable one is finer (or coarser) than the other.