Universal homogeneous event structures and domains

Abstract

In the theory of denotational semantics of programming languages, several authors established the existence of particular kinds of “universal” domains. Here, we use a general model-theoretic result to show that there exists a unique countable universal homogeneous event structure. From this, we deduce that the category of all event domains, with stable embedding-projection pairs as morphisms, contains a universal object. Similarly, we also obtain a universal dI-domain. We also show that the category of all event domains is closed under inverse limits. Similar results are derived for Kahn and Plotkin's concrete data structures and concrete domains.