Total sets and objects in domain theory

Annals of Pure and Applied Logic 60 (2):91-117 (1993)
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Abstract

Berger, U., Total sets and objects in domain theory, Annals of Pure and Applied Logic 60 91-117. 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 Heriditarily Effective Operations

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References found in this work

Theorie der Numerierungen I.Ju L. Eršov - 1973 - Mathematical Logic Quarterly 19 (19‐25):289-388.
Theorie der Numerierungen II.J. U. L. Eršov - 1975 - Mathematical Logic Quarterly 21 (1):473-584.
Countable functionals.S. C. Kleene - 1959 - Journal of Symbolic Logic 27 (3):81--100.

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