Dilworth’s Decomposition Theorem in the Infinite Case

Utility Representation of an Incomplete Preference Relation

“…Consequently, in what follows, we shall also examine conditions this theorem by using Rado's selection principle. Several alternative proofs have been since then furnished; the most direct proof that I know deduces the result readily from the finite case by applying Gödel's compactness theorem (Milner, 1990).…”