John Brzozowski, Jay Lou, Radu Negulescu,
A Characterization of Finite Ternary Algebras,
Technical Report CS-96-26,
Department of Computer Science,
University of Waterloo,
Waterloo, Ontario, Canada N2L 3G1,
9 pp., 1996.

Abstract

A ternary algebra is a De Morgan algebra (that is, a distributive lattice with 0 and 1 and a complemene operation that satisfies De Morgan's laws) with an additional constant Phi satisfying Phi=-Phi, (a+(-a))+Phi=a+(-a), and a*(-a)*Phi=a*(-a). We provide a characterization of finite ternary algebras in terms of "subset-pair algebras", whose elements are pairs (X, Y) of subsets of a given base set E, which have the property XUY=E, and whose operations are based on simple set operations.

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