Object-oriented applications of database systems require database tran
sformations involving nonstandard functionalities such as set manipula
tion and object creation, that is, the introduction of new domain elem
ents. To deal with these functionalities, Abiteboul and Kanellakis [19
89] introduced the ''determinate'' transformations as a generalization
of the standard domain-preserving transformations. The obvious extens
ions of complete standard database programming languages, however, are
not complete for the determinate transformations. To remedy this mism
atch, the ''constructive'' transformations are proposed. It is shown t
hat the constructive transformations are precisely the transformations
that can be expressed in said extensions of complete standard languag
es. Thereto, a close correspondence between object creation and the co
nstruction of hereditarily finite sets is established. A restricted ve
rsion of the main completeness result for the case where only list man
ipulations are involved is also presented.