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Some applications of computable one-one numberings

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Abstract

We present a simple proof of a Theorem of Khutoretskij on the number of incomparable one-one numberings of an r.e. family of r.e. sets. The proof directly generalizes to effective domains. In the second part, applying a Theorem of Goncharov, we show that for anyk≧ there exist total recursive functions having exactlyk recursive isomorphism classes. Using a Theorem of Selivanov, it is shown that a certain notion of computability via gödelization is different from Lacombe's notion ofV-recursiveness. Finally, we discuss the complexity (w.r.t.T-degrees) of translating a Gödelnumbering into a direct sum of Friedbergnumberings.

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  1. Institut für Logik, Komplexität und Deduktionssysteme, Universität Karlsruhe, Postfach 6980, W-7500, Karlsruhe 1, Federal Republic of Germany

    Martin Kummer

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  1. Martin Kummer
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Kummer, M. Some applications of computable one-one numberings. Arch Math Logic 30, 219–230 (1990). https://doi.org/10.1007/BF01792984

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  • DOI: https://doi.org/10.1007/BF01792984

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