Tω as a Universal Domain

摘要

In mathematical semantics, in the sense of Scott, the question arises of what domains of interpretation should be chosen. It has been felt by the author, and others, that lattices are the wrong choice and instead one should use complete partial orders (cpo's), which do not necessarily have the embarrassing top element. So far, however, no mathematical theory as pleasant as that developed for Pω in the paper “Data Types as Lattices” has been available. The present paper is intended to fill this gap and is a close analog of the Pω paper, replacing Pω by Tω, the ω-power of the three-element truthvalue cpo, T.