For every set formula_1 of elements of formula_2, the algebraically independent subsets of formula_1 satisfy the axioms that define the independent sets of a matroid. In this matroid, the rank of a set of elements is its transcendence degree, and the flat generated by a set formula_48 of elements is the intersection of formula_2 with the field formula_3. A matroid that can be generated in this way is called an algebraic matroid. No good characterization of algebraic matroids is known, but certain matroids are known to be non-algebraic; the smallest is the Vámos matroid.