On an Algebra of Sets of Finite Sequences

The algebras studied in this paper were suggested to the author by William Craig as a possible substitute for cylindric algebras. Both kinds of algebras may be considered as algebraic versions of first-order logic. Cylindric algebras can be introduced as follows. Let Y be a first-order language, and let % be an Y-structure. We assume that Y has a simple infinite sequence v0, vi, . * * of individual variables, and we take as known what it means for a sequence x = of elements of % to satisfy a formula b of Y in A. Let He be the collection of all sequences x