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An iterative description of the class ξ′ of Grzegorczyk's hierarchy

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Abstract

A class of abstract computing machines is described. It is proved that the class of all functions computable by these machines coincides with the class ξ′ of Grzegorczyk's hierarchy.

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Literature cited

  1. A. A. Muchnik, “On two approaches to classical recursive functions,” in: Problems in Mathematical Logic [in Russian], Moscow, pp. 123–138 (1970).

  2. N. P. Astanina, “The class of functions computable by a two-way deterministic automaton with storage memory,” Third All-Union Conference on Mathematical Logic, (June 23–27, 1974), Thesis, Novosibirsk (1974).

  3. A. Grzegorczyk, “Some classes of recursive functions,” Rozpr. Mat., IV,Warsaw (1957).

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  4. S. V. Paxomov, “One simple syntactical definition of all of the Grzegorczyk hierarchy,” Zap. Nauch. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,40, 127–130 (1974).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo. Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 60, pp. 3–14, 1976. Results presented April 24, 1975.

The author would like to acknowledge the assistance of N. K. Kosovskii whosuggested the direction of this work and helped check and formulate the results of this paper.

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Bel'tyukov, A.P. An iterative description of the class ξ′ of Grzegorczyk's hierarchy. J Math Sci 14, 1429–1436 (1980). https://doi.org/10.1007/BF01693973

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  • DOI: https://doi.org/10.1007/BF01693973

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