Some independence results for control structures in complete numberings

Journal of Symbolic Logic 66 (1):357-382 (2001)
Abstract
Acceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied, among others by Riccardi and Royer, how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Eršov
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DOI 10.2307/2694927
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Theorie der Numerierungen I.Ju L. Eršov - 1973 - Mathematical Logic Quarterly 19 (19‐25):289-388.
Inductive Inference and Computable One-One Numberings.Rsinš Freivalds, Efim B. Kinber & Rolf Wiehagen - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (27-32):463-479.

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