Domains in H

AbstractWe give various internal descriptions of the category ω-Cpo of ω-complete posets and ω-continuous functions in the model H of Synthetic domain theory introduced in Fiore and Rosolini (J. Pure Appl. Algebra 116 (1997) 151–162). It follows that the ω-cpos lie between the two extreme synthetic notions of domain given by repleteness and well-completeness