  In this paper, we investigate the algebras of consequence operators and
finite consequence operators on a fixed language. Significant new collections
of consequence operators are defined and shown to be complete and distributive
sublattices. Further, the collection of consequence operators is shown to be
almost atomic. Other lattice theoretic properties are investigated and useful
chain properties are obtained. In the last section, natural languages, and
associated consequence operators, are encoded and embedded into a nonstandard
structure. The entire basic theory of nonstandard consequence operators is
developed in this last section.
