A direct characterization of completion

Abstract

Canonical Completion of a poset is of central importance in obtaining fully abstract semantic models. Stoughton, in his thesis, has described a completion technique. In this short note, we provide a direct characterization of the cpo constructed using this technique. This characterization shows that the completed poset consists of all closed continuously directed subsets of the original poset and vice versa. This result is stated as a conjecture by Stoughton.