  The theory of bounded, distributive lattices provides the appropriate
language for describing directionality and asymptotics in dynamical systems.
For bounded, distributive lattices the general notion of `set-difference'
taking values in a semilattice is introduced, and is called the Conley form.
The Conley form is used to build concrete, set-theoretical models of spectral,
or Priestley spaces, of bounded, distributive lattices and their finite
coarsenings. Such representations build order-theoretic models of dynamical
systems, which are used to develop tools for computing global characteristics
of a dynamical system.
