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A reduction of the recursion scheme

Published online by Cambridge University Press:  12 March 2014

M. D. Gladstone
M. D. Gladstone*
Affiliation:
University of Bristol, England
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Extract

The class of primitive recursive functions may be defined as the closure of certain initial functions, namely the zero, successor and identity functions, under two schemes, namely composition (sometimes called “substitution”) and recursion. For a detailed definition the reader is referred to any standard work, for instance p. 219 of [2], by Kleene.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 4 , February 1968 , pp. 505 - 508
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Goodstein, R. L., Recursive number theory, North-Holland, Amsterdam, 1964.Google Scholar
[2]Kleene, S. C., Introduction to metamathematics, North-Holland, Amsterdam, 1959.Google Scholar
[3]Robinson, R. M., Primitive recursive functions. Bulletin of the American Mathematical Society, vol. 53 (1947), pp. 925–942.CrossRefGoogle Scholar