The category of cpos from a synthetic viewpoint


            Marcelo Fiore                      Giuseppe Rosolini

     LFCS, University of Edinburgh         Dipartimento di Matematica
         The King's Buildings                  via Dodecaneso 35 
      Edinburgh EH9 3JZ, Scotland             16146 Genova, Italy


                                  Abstract

  We provide an internal characterization of the category w-Cpo of 
  w-complete posets and w-continuous functions within the model H of SDT 
  recently introduced by the authors.  It follows that w-cpos lie between 
  the two extreme synthetic notions of domain given by repleteness and 
  well-completeness.