Consistent Hoare powerdomains over dcpos

In this paper, we show that the consistent Hoare powerdomain Hc(P) over a dcpo P exists and is isomorphic to a special Scott closed subset of Γ(P) relative to the Scott topology σ(Γ(P)), where Γ(P) is the collection of all nonempty Scott closed subsets of P ordered by the set-theoretic inclusion relation.