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Canonical recursive functions and operations

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Abstract

A series of properties of canonical recursive functions and operations are established, allowing the possibility of extrapolating to these functions and operations the method proposed by R. L. Goodstein for constructing equational calculi.

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Literature cited

  1. S. C. Kleene, Introduction to Metamathematics, Amsterdam (1952).

  2. A. I. Mal'tsev, Algorithms and Recursive Functions [in Russian], Moscow (1965).

  3. M. L. Minsky, Finite and Infinite Machines, Englewood Cliffs, New Jersey (1967).

  4. R. L. Goodstein, Recursive Number Theory, Amsterdam (1957).

  5. N. A. Shanin, “Hierarchy of methods of understanding inferences in constructive mathematics,” Tr. Mat. Inst. Akad. Nauk SSSR,129, 203–266 (1973).

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  6. Z. Manna, Mathematical Theory of Computation, New York (1974).

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Authors
  1. N. A. Shanin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 218–235, 1979.

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Shanin, N.A. Canonical recursive functions and operations. J Math Sci 20, 2381–2390 (1982). https://doi.org/10.1007/BF01629451

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  • DOI: https://doi.org/10.1007/BF01629451

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