  We introduce and explore Rafael Sorkin's \textit{evolving co-event scheme}: a
theoretical framework for determining completely which events do and do not
happen in evolving quantum, or indeed classical, systems. The theory is
observer-independent and constructed from discrete histories, making the
framework a potential setting for discrete quantum cosmology and quantum
gravity, as well as ordinary discrete quantum systems. The foundation of this
theory is Quantum Measure Theory, which generalises (classical) measure theory
to allow for quantum interference between alternative histories; and its
co-event interpretation, which describes whether events can or can not occur,
and in what combination, given a system and a quantum measure. In contrast to
previous co-event schemes, the evolving co-event scheme is applied in stages,
in the stochastic sense, without any dependence on later stages, making it
manifestly compatible with an evolving block view. It is shown that the
co-event realities produced by the basic evolving scheme do not depend on the
inclusion or exclusion of zero measure histories in the history space, which
follows non-trivially from the basic rules of the scheme. It is also shown that
this evolving co-event scheme will reduce to producing classical realities when
it is applied to classical systems.
