Flat Axioms for Matroids is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a finite set, and let be a collection of subsets of satisfying the following three axioms: 1. . 2. If is nonempty, then . 3. For every , let \begin{align } \mathcal C(F) := \{G \in \mathcal F : F \subsetneq G \text{ and there is no.