Using the well-known equivalence between meet-completions of posets and
standard closure operators we show a general method for constructing
meet-completions for isotone poset expansions. With this method we find a
meet-completion for ordered domain algebras which simultaneously serves as the
base of a representation for such algebras, thereby proving that ordered domain
algebras have the finite representation property. We show that many of the
equations defining ordered domain algebras are preserved in this completion but
associativity, (D2) and (D6) can fail