STONE SPACE OF CYLINDRIC ALGEBRAS AND TOPOLOGICAL MODEL SPACES

摘要

The Stone representation theorem was a milestone for the understanding of Boolean algebras. From Stone's theorem, every Boolean algebra is representable as a field of sets with a topological structure. By means of this, the structural elements of any Boolean algebra, as well as the relations between them, are represented geometrically and can be clearly visualized. It is no different for cylindric algebras: Suppose that A is a cylindric algebra and S is the Stone space of its Boolean part. (Among the elements of the Boolean part are the diagonal elements.) It is known that with nothing more than a family of equivalence relations on S to represent quantifiers, S represents the full cylindric structure just as the Stone space alone represents the Boolean structure. S with this structure is called a cylindric space.