An Extension of Models of Axiomatic Domain Theory 
                to Models of Synthetic Domain Theory

           Marcelo P. Fiore          Gordon D. Plotkin
           <mf@dcs.ed.ac.uk>         <gdp@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

                           October 1996

                             Abstract

We relate certain models of Axiomatic Domain Theory (ADT) and Synthetic
Domain Theory (SDT).  On the one hand, we introduce a class of 
non-elementary models of SDT and show that the domains in them yield
models of ADT.  On the other hand, for each model of ADT in a wide 
class we construct a model of SDT such that the domains in it provide a
model of ADT which conservatively extends the original model.