to the family. A matroid belongs to the family if and only if it does not have a forbidden matroid as a minor. Often, but not always, the set of forbidden matroids is finite, paralleling the Robertson-Seymour theorem which states that the set of forbidden minors of a minor-closed graph family is always finite.

An example of this phenomenon is given by the regular matroids, matroids that are representable over all fields. Equivalently a matroid