Another usage of "complete meet-semilattice" refers to a bounded complete cpo. A complete meet-semilattice in this sense is arguably the "most complete" meet-semilattice that is not necessarily a complete lattice. Indeed, a complete meet-semilattice has all "non-empty" meets (which is equivalent to being bounded complete) and all directed joins. If such a structure has also a greatest element (the meet of the empty set), it is also a complete lattice. Thus a complete semilattice turns out to be "a complete lattice possibly lacking a top". This definition is of interest specifically in domain theory, where bounded complete algebraic cpos are studied as Scott domains. Hence Scott domains have been called "algebraic semilattices".