  We continue our efforts to understand, within the framework of the quantum
mechanics of the universe as a whole, the quasiclassical realm of familiar
experience as a feature emergent from the Hamiltonian of the elementary
particles and the initial condition of the universe. Quantum mechanics assigns
probabilities to exhaustive sets of alternative decoherent histories of the
universe. We introduce and define the notion of strong decoherence. We replace
the notion of maximal sets of alternative decohering histories by defining the
more useful concept of "full" sets of alternative strongly decohering
histories. These full sets fall into equivalence classes each of which is
characterized by a basis in Hilbert space. Finally we describe our continuing
efforts to find measures of classicality --- measures that could be applied to
such full sets of alternative strongly decohering so as to characterize a
quasiclassical realm.
