Complete Cuboidal Sets in Axiomatic Domain Theory


      Marcelo Fiore            Gordon Plotkin               John Power
    <mf@dcs.ed.ac.uk>        <gdp@dcs.ed.ac.uk>          <ajp@dcs.ed.ac.uk>

                       Department of Computer Science 
                Laboratory for Foundations of Computer Science 
                University of Edinburgh, The King's Buildings 
                        Edinburgh EH9 3JZ, Scotland 


                                 Abstract

We study the enrichment of models of axiomatic domain theory.  To this end, we
introduce a new and broader notion of domain, viz. that of complete cuboidal
set, that complies with the axiomatic requirements.  We show that the category
of complete cuboidal sets provides a general notion of enrichment for a wide 
class of axiomatic domain-theoretic structures.