Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?

The form of the interaction Hamiltonian between the apparatus and its environment is sufficient to determine which observable of the measured quantum system can be considered "recorded" by the apparatus. The basis that contains this record---the pointer basis of the apparatus---consists of the eigenvectors of the operator which commutes with the apparatus-environment interaction Hamiltonian. Thus the environment can be said to perform a nondemolition measurement of an observable diagonal in the pointer basis.