On stable domains

Abstract

In denotational semantics of programming languages, various categories of domains, with continuous functions as morphisms, and their closure properties under operations like taking products or function space have been intensively studied. However, classes of domains which, like bifinite domains, are also closed under the Plotkin powerdomain operation are rare. Here we investigate stable domains. They naturally generalize the concept of dI-domains studied by Berry and others and satisfy a strong finiteness condition for compact elements, but in general no distributivity assumption. These classes recently were shown (in joint work with R. Göbel) to contain universal objects. We first derive an order-theoretic characterization of stability and then show that the class of all stable domains is closed under countable cartesian products, stable function space and the Plotkin powerdomain operation. As a consequence, we also obtain that the categories of all stable L-domains and of all distributive stable L-domains, with stable functions as morphisms, are cartesian-closed.