On Matroid Theorems of Edmonds and Rado

Introduction In this note I show how very general and powerful results about the union and intersection of matroids due to J. Edmonds [19] may be deduced from a matroid generalisation of Hall's theorem by R. Rado [13]. Throughout, S, T, will denote finite sets, |X| will denote the cardinality of the set X and {xt: iel} denotes the set whose distinct elements are the elements x{. A matroid (S, M) is a finite set S together with a family M of subsets of S, called independent sets, which satisfies the following axioms