A CHARACTERIZATION OF de MORGAN ALGEBRAS

Abstract

In this note we show that every de Morgan algebra is isomorphic to a two-subset algebra, < P,⊔,⊓,~,0P,1P>, where P is a set of pairs (X,Y) of subsets of a set I, (X,Y)⊔ (X′,Y′)=(X∩ X′,Y∪ Y′),(X,Y) ⊓ (X′,Y′)=(X∪ X′,Y∩Y′),~(X,Y)= (Y,X), 0P=(I,∅) and 1P=(∅,I). This characterization generalizes a previous result that applied only to a special type of de Morgan algebras called ternary algebras.