Event Structures Representing Domains with Coherence 1995

Abstract:  We present two cartesian closed subcategories of dIC, the category of dI domains with coherence and strongly stable maps introduced in [2, 3] to provide an extensional and "sequential" model of PCF ([7]). The interest of these subcategories lies in the fact that the order structure of their objects is decomposed in two logically independent parts: the order on prime elements and the coherence predicate on them. This leads to a simplified description of these domains, in terms of suitable classes of event structures. keywords: denotational semantics, sequentiality, stability, strong stability, hypercoherences, event strucures. 1 Introduction The category of dI-domains with coherence and strongly stable functions (dIC) introduced and studied in [2, 3] provides a model of PCF ([7]) in which first-order morphisms are sequential in the sense of Kahn-Plotkin ([6]) and in which morphisms are functions "in extenso". The new feature of these structures is that domains are endowed with a coher...