The Largest Cartesian Closed Category of Stable Domains

Berry's category of dI-domains with stable functions is a relatively intricate , yet elegant framework for semantics of programming languages. Despite over fteen years of work in the area, the exact reasons for dis-tributivity (Axiom d) and nitariness (Axiom I) have not been fully ex-plicated. This paper shows that Axiom d and Axiom I are important when one works within the realm of Scott-domains. In particular, it has been shown that (i) if D ! s D] has a countable basis, then D must be nitary, for any Scott-domain D; (ii) if D ! s D] is bounded complete, then D must be distributive, for any nitary Scott-domain D. Therefore, the category of dI-domains is the largest cartesian closed category within omega-algebraic, bounded complete domains, with the exponential being the stable function space.