  This dissertation investigates questions arising in the consistent histories
formulation of the quantum mechanics of closed systems. Various criteria for
approximate consistency are analysed. The connection between the
Dowker-Halliwell criterion and sphere packing problems is shown and used to
prove several new bounds on the violation of probability sum rules. The quantum
Zeno effect is also analysed within the consistent histories formalism and used
to demonstrate some of the difficulties involved in discussing approximate
consistency. The complications associated with null histories and infinite sets
are briefly discussed.
  The possibility of using the properties of the Schmidt decomposition to
define an algorithm which selects a single, physically natural, consistent set
for pure initial density matrices is investigated. The problems that arise are
explained, and different possible algorithms discussed. Their properties are
analysed with the aid of simple models. A set of computer programs is described
which apply the algorithms to more complicated examples.
  Another algorithm is proposed that selects the consistent set (formed using
Schmidt projections) with the highest Shannon information. This is applied to a
simple model and shown to produce physically sensible histories. The theory is
capable of unconditional probabilistic prediction for closed quantum systems,
and is strong enough to be falsifiable. Ideas on applying the theory to more
complicated examples are discussed.
