  We lay a comprehensive foundation for the study of redundant information
storage in decoherence processes. Redundancy has been proposed as a
prerequisite for objectivity, the defining property of classical objects. We
consider two ensembles of states for a model universe consisting of one system
and many environments: the first consisting of arbitrary states, and the second
consisting of ``singly-branching'' states consistent with a simple decoherence
model. Typical states from the random ensemble do not store information about
the system redundantly, but information stored in branching states has a
redundancy proportional to the environment's size. We compute the specific
redundancy for a wide range of model universes, and fit the results to a simple
first-principles theory. Our results show that the presence of redundancy
divides information about the system into three parts: classical (redundant);
purely quantum; and the borderline, undifferentiated or ``nonredundant,''
information.
