Cartesian closed categories of separable Scott domains

Abstract

We classify all sub-cartesian closed categories of the category of separable Scott domains. The classification employs a notion of coherence degree determined by the possible inconsistency patterns of sets of finite elements of a domain. Using the classification, we determine all sub-cartesian closed categories of the category of separable Scott domains that contain a universal object. The separable Scott domain models of the λβ-calculus are then classified up to a retraction by their coherence degrees.