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Final Report 3
By Jim Chaffee

Appendix
A Brouwerian lattice is a lattice in which for any given pair of elements a and b, the set of all elements whose meet with the first element is bounded by the second has a greatest element, called the relative pseudo-complement of a in b.
All Brouwerian lattices are distributive. A Brouwerian logic is a Brouwerian lattice. Note that the open sets in a topological space form a Brouwerian lattice. A Brouwerian lattice is a Boolean algebra if either not not x is x for all x or else if x and not x is zero for all x.
A quantum logic is a complete, atomic, orthomodular lattice isomorphic to the lattice of all closed subspaces of a separable Hilbert space.
The code lattices are inherently self-contradictory. The Brouwerian implication is not the classical implication and all closed subsets of the real line do not form a Brouwerian lattice. Since this inherent contradiction is impossible, the received codes cannot exist.

©Jim Chaffee 2005

