DI-domains as information systems

Abstract

This paper introduces stable information systems. Stable information systems determine dI-domains and stable approximable mappings give stable functions, and vice versa. The notion of rigid embedding is captured by a subsystem relation. Under this relation, stable information systems form a cpo. Constructions like lifting, sum, product and function space are proposed which induce continuous functions on the cpo. In this way recursive stable information systems can be defined using fixed point theory.