  Perhaps surprisingly, given that constructions like this provide complements for all sets, they give a central rôle to the concept of wellfounded set in that the wellfounded sets of the new model can be made to be an isomorphic copy of the wellfounded sets in the structure one starts with. Further, these models satisfy a scheme of replacement for wellfounded sets: anything the same size as a wellfounded set is a set. (Replacement for, say, wellordered sets doesn’t come free in the same way)