A Representation of SFP

This chapter introduces a representation of the category of SFP domains. It uses structures similar to but more general than Scott’s information systems. Distilled from Gentzen’s sequent calculi, a basic structure called a sequent structure is produced. Sequent structures determine a major part of the axioms of information systems. A category of special kind of sequent structures called the strongly finite ones is shown to be equivalent to the category of SFP domains. Constructions like the Plotkin power domain and the function space are given, as well as a complete partial order of such structures to give solutions to recursively defined systems.