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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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 $ 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$).


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DOI: https://doi.org/10.1090/S0002-9947-1988-0961607-5
Article copyright: © Copyright 1988 American Mathematical Society