  Recently 't Hooft demonstrated that ``For any quantum system there exists at
least one deterministic model that reproduces all its dynamics after
prequantization''. An extension is presented here which covers quantum systems
that are characterized by a complete set of mutually commuting Hermitian
operators (``beables''). We introduce the symmetry of beables: any complete set
of beables is as good as any other one which is obtained through a real general
linear group transformation. The quantum numbers of a specific set are related
to symmetry breaking initial and boundary conditions in a deterministic model.
The Hamiltonian, in particular, can be taken as the emergent beable which
provides the best resolution of the evolution of the model universe.
