A Stone-type representation theorem for algebras of relations of higher rank
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- by H. Andréka and R. J. Thompson PDF
- Trans. Amer. Math. Soc. 309 (1988), 671-682 Request permission
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 $n$-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 $n$).References
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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