Axiom:Rank Axioms (Matroid)

Definition
Let $S$ be a finite set.

Let $\rho : \powerset S \to \Z$ be a mapping from the power set of $S$ into the integers.

Formulation 1
$\rho$ is said to satisfy the rank axioms :

Formulation 2
$\rho$ is said to satisfy the rank axioms :

Also see

 * Equivalence of Definitions of Matroid Rank Axioms