  The immensely fruitful concept of Grothendieck topology or covering issued
from the efforts of algebraic geometers to study "sheaf-like" objects defined
on categories more general than the lattice of open sets on a topological
space. In the present paper the covering concept - here called a cover scheme
-is presented and developed in the simple case when the underlying category is
a preordered set. The relationship between cover schemes, frames (complete
Heyting algebras), Kripke models, and frame-valued set theory is discussed.
Finally cover schemes and frame-valued set theory are applied in the context of
Markopoulou's 1999 account of discrete spacetime as sets "evolving" over a
causal set.
