Definition:Independence System

Definition
Let $S$ be a finite set.

Let $\mathscr F$ be a set of subsets of $S$ satisfying the independence system axioms:

The ordered pair $I = \struct {S, \mathscr F}$ is called an independence system on $S$.

Also known as
When the context is obvious, $I = \struct {S, \mathscr F}$ is simply called an independence system.