Internal injectivity of Boolean algebras in MSet

This paper deals with the internal notion of injectivity for Boolean algebras in the topos of M-sets. Given that, for ordinary Boolean algebraas, injectivity is the same as completeness (Sikorski's theorem) and the injective hull is the same as normal completion, we investigate here how the internal notion of completeness relates to internal injectivity. Further, we consider the internal injectivity of the initial Boolean algebra 2 which is equivalent to the prime ideal theorem for Boolean algebras in this topos. Before we turn specificially to Boolean algebras, we develop the bassic general facts concerning internal injectivity in MSet for arbitrary equational classes of algebras.