A Set Theoretic Treatment of Coherent Systems

Abstract

This paper develops properties of coherent systems from a set theoretic viewpoint with particular emphasis on modules of coherent systems. The methods used here demonstrate concisely the previously reported properties of modules as well as some new properties. Specifically, min path sets and min cut sets of a coherent system are given several characterizations. The modularity of a subset of components is given a new characterization which we use as a definition. The situation under which a set and its complement are simultaneously modules is characterized. Finally, the established three modules theorem is given a new proof.