A General Extension Theorem for Binary Relations

Abstract

A general theorem on “extending” binary relations to linear (or strict linear) orders is proved. The well-known result that every partial order can be written as the intersection of linear orders in which it is embedded is obtained as a special case, as are several other extension theorems of this type. Using duality arguments, a number of results on the composition of binary relations are proved. For example, a complete, negatively transitive relation is the union of all linear orders embedded within it.Journal of Economic LiteratureClassification Number: C60.

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