Definition:Matroid Axioms

Definition
Let $S$ be a finite set.

Let $\mathscr I$ be a set of subsets of $S$.

The matroid axioms are the conditions on $S$ and $\mathscr I$ in order for the ordered pair $\struct {S, \mathscr I}$ to be a matroid:

Also see

 * Equivalence of Definitions of Matroid where it is shown that each of the above sets of axioms are equivalent.