On the Order–completion of Additive Conjoint Structures

Measurement theory provides additive conjoint structures for additive representations of empirical data. Roughly, an additive conjoint structure is a product of (quasi)ordered sets with some properties connecting the different factors of the product. Well-known Debreu’s Theorem says that every additive conjoint structure can be embedded in a vector space over the real numbers. This embedding yields a completion of the additive conjoint structure where every factor becomes a complete lattice. This paper introduces a synthetical way of constructing this completion without using real numbers.