# Category:Axioms/Matroid Theory

This category contains axioms related to Matroid Theory.

Let $M = \struct {S, \mathscr I}$ be an independence system.

$M$ is called a matroid on $S$ if and only if $M$ also satisfies:

 $(\text I 3)$ $:$ $\ds \forall U, V \in \mathscr I:$ $\ds \size V < \size U \implies \exists x \in U \setminus V : V \cup \set x \in \mathscr I$

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Axioms/Matroid Theory"

The following 5 pages are in this category, out of 5 total.