Mathematics of multisets in the Fraenkel-Mostowski framework

Abstract

We present multisets in the framework of the Fraenkel-Mostowski set theory. We extend the notion of multiset over a nite alphabet by considering the notion of algebraically nitely supported multiset over a possibly innite alphabet. We study the correspondence between some properties of multisets obtained in the Fraenkel-Mostowski framework (where only nitely supported elements are allowed) and those obtained in the classical ZermeloFraenkel framework.