  For representation by partial functions in the signature with intersection,
composition and antidomain, we show that a representation is meet complete if
and only if it is join complete. We show that a representation is complete if
and only if it is atomic, but that not all atomic representable algebras are
completely representable. We show that the class of completely representable
algebras is not axiomatisable by any existential-universal-existential
first-order theory. By giving an explicit representation, we show that the
completely representable algebras form a basic elementary class, axiomatisable
by a universal-existential-universal sentence.
