Terms in cylindric algebras

Abstract

Abstract.A new algebraic treatment of terms within the framework of cylindric algebras.The theory of terms in locally finite polyadic algebras of infinite degree has been developed by Paul Halmos [2] and Aubert Daigneault [1]. In this paper we present a simple, new treatment of terms in dimension complemented cylindric algebras of infinite degree. By taking advantage of the presence of diagonal elements (which cannot be assumed to exist in arbitrary polyadic algebras), and by exploiting the well-known correspondence between operations and predicates which are single-valued in one of their variable places, we are able to introduce terms in a manner which is direct, well motivated and easy to use.

On the structure of Lindenbaum algebras: an approach using algebraic logic

“…For a full discussion of terms in cylindric algebras the reader is referred to [4]; however, for the present purposes only a few rudimentary notions are needed. An element x G A will be called "diagonal-like" if it has the following two properties for some k < a:…”