SET-BASED ORDERING ON SIMPLE MULTISETS OF INCOMPARABLE OBJECTS

Abstract

It is convincing that there exists an ordering on simple multisets of incomparable objects by means of the Jouannaud-Lascanne set-based multiset ordering. A successful attempt to show that a singleton multiset is dominated by a simple pair multiset despite the incomparability of their objects is made with respect to the ordering. Furthermore, an existence of the ordering among simple multisets of higher cardinalities where the cardinality of the preceding multiset is a unit or more less than that of the succeeding multiset is observed. Thus, we obtain an extension of the ordering to simple multisets of incomparable objects. No stronger set-based multiset ordering may be found to exist.