  We consider complete lattices equipped with preorderings indexed by the
ordinals less than a given (limit) ordinal subject to certain axioms. These
structures, called stratified complete lattices, and weakly monotone functions
over them, provide a framework for solving fixed point equations involving
non-monotone operations such as negation or complement, and have been used to
give semantics to logic programs with negation.
  More precisely, we consider stratified complete lattices subject to two
slightly different systems of axioms defining `models' and `strong models'. We
prove that a stratified complete lattice is a model iff it is isomorphic to the
stratified complete lattice determined by the limit of an inverse system of
complete lattices with `locally completely additive' projections. Moreover, we
prove that a stratified complete lattice is a strong model iff it is isomorphic
to the stratified complete lattice determined by the limit of an inverse system
of complete lattices with completely additive projections.
  We use the inverse limit representation to give alternative proofs of some
recent results and to derive some new ones for models and strong models. In
particular, we use the representation theorem to prove that every model gives
rise to another complete lattice structure, which in limit models corresponds
to the lexicographic order. Moreover, we prove that the set of all fixed points
of a weakly monotone function over a model, equipped with the new ordering, is
a complete lattice. We also consider symmetric models that satisfy, together
with each axiom, the dual axiom, and use the inverse limit representation to
prove that every strong model is symmetric.
