A Stone-type representation theorem for algebras of relations of higher rank
Hajnal Andréka, Richard Joel Thompson · Transactions of the American Mathematical Society · 1988
The Stone representation theorem for Boolean algebras gives us a finite set of equations axiomatizing the class of Boolean set algebras. Boolean set algebras can be considered to be algebras of unary relations. As a contrast here we investigate algebras of n n -ary relations (originating with Tarski). The new algebras have more operations since there are more natural set theoretic operations on n n -ary relations than on unary ones. E.g. the identity relation appears as a new constant. The Resek-Thompson theorem we prove here gives a finite set of equations axiomatizing the class of algebras of n n -ary relations (for every ordinal n n ).