Total Sets and Objects in Domain Theory
Ulrich Berger

Abstract
Total sets and objects generalizing total functions are introduced into the theory of effective domains of Scott and Ersov. Using these notions Kreisel's Density Theorem and the Theorem of Kreisel-Lacombe-Shoenfield are generalized. As an immediate consequence we obtain the well known continuity of computable functions on the constructive reals as well as a domain theoretic characterization of the Hereditarily Effective Operations.

Bib entry

@Article{Berger93,
  author = 	"Ulrich Berger",
  title = 	"Total Sets and Objects in Domain Theory",
  journal = 	"Annals of Pure and Applied Logic",
  year = 	"1993",
  volume = 	"60",
  pages = 	"91--117"}

Draft copy