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A Stone type representation theorem for algebras of relations of higher rank. (English) Zbl 0707.03053
Summary: 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-ary relations (originating with Tarski). The new algebras have more operations since there are more natural set theoretic operations on 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-ary relations (for every ordinal n).

MSC:
03G15 Cylindric and polyadic algebras; relation algebras
03C95 Abstract model theory
03G25 Other algebras related to logic
03C75 Other infinitary logic
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