Definition:Minimal Condition/Subset Ordering

Definition
Let $S$ be a set.

Let $F$ be a set of subsets of $S$.

Let $F$ be ordered by the subset relation.

Then $S$ satisfies the minimal condition on $F$ $F$ satisfies the minimal condition.

Also see

 * Definition:Descending Chain Condition
 * Definition:Maximal Condition on Submodules