A Stone-type representation theorem for algebras of relations of higher rank

Authors:
H. Andréka and R. J. Thompson

Journal:
Trans. Amer. Math. Soc. **309** (1988), 671-682

MSC:
Primary 03G15; Secondary 03C95, 03G25

DOI:
https://doi.org/10.1090/S0002-9947-1988-0961607-5

MathSciNet review:
961607

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Abstract: 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 -ary relations (originating with Tarski). The new algebras have more operations since there are more natural set theoretic operations on -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 -ary relations (for every ordinal ).

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DOI:
https://doi.org/10.1090/S0002-9947-1988-0961607-5

Article copyright:
© Copyright 1988
American Mathematical Society