Cylindric algebras and algebras of substitutions
Charles C. Pinter · Transactions of the American Mathematical Society · 1973
Several new formulations of the notion of cylindric algebra are presented. The class $C{A_\alpha }$ of all cylindric algebras of degree $\alpha$ is shown to be definitionally equivalent to a class of algebras in which only substitutions (together with the Boolean $+ , \cdot$, and $-$) are taken to be primitive operations. Then $C{A_\alpha }$ is shown to be definitionally equivalent to an equational class of algebras in which only substitutions and their conjugates (together with $+ , \cdot$, and $-$) are taken to be primitive operations.