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Simplifications of the recursion scheme

Published online by Cambridge University Press:  12 March 2014

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

This paper resolves 3 problems left open by R. M. Robinson in [3].

We recall that the set of primitive recursive functions is the closure under (i) substitution (or “composition”), and (ii) recursion, of the set P consisting of the zero, successor and projection functions (see any textbook, for instance p. 120 of [2]).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 4 , December 1971 , pp. 653 - 665
Copyright
Copyright © Association for Symbolic Logic 1972

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References

[1]Gladstone, M. D., A reduction of the recursion scheme, this Journal, vol. 32 (1967), pp. 505–508.Google Scholar
[2]Mendelson, Elliott, Introduction to mathematical logic, van Nostrand, Princeton, N J., 1964.Google Scholar
[3]Robinson, R. M., Primitive recursive functions, Bulletin of the American Mathematical Society, vol. 53 (1947), pp. 925–942.CrossRefGoogle Scholar