Group-valued charges: common extensions and the infinite Chinese remainder property

Abstract

We exhibit two consistent, integer-valued charges (finitely additive measures) which do not have a common, integer-valued extension. More generally, after introducing the notion of an infinitary Chinese remainder property for Abelian groups, we show that if a group has the common extension property, then the group must have the infinite Chinese remainder property. The class of groups with the common extension property is characterised as coincident with the class of cotorsion groups.