Semiorders and the Theory of Choice: A Correction

Abstract

The article clarifies some theorems and mathematical models proposed for semiorders and the theory of choice. Restrictions were analyzed which were necessary and sufficient to ensure that the ordering revealed by the choice function would be a semiorder. A problem was encountered relevant to the assumption that certain choice sets were nonempty. Modified versions of Axioms four, five and six were given with a statement of Lemma five. Evidently, the alternative proof of Theorem three has the advantages over the proof of less redundance in the axioms and of factoring the semiorder proof into the separate proofs for interval orders and semitransitive orders.