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On n-adic representation of numbers1

Published online by Cambridge University Press:  12 March 2014

Thomas E. Patton
Thomas E. Patton*
Affiliation:
The University of Pennsylvania
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Extract

In Smullyan [1], where recursive enumerability is defined in terms of elementary dyadic arithmetics (dyadic EA's), it is shown that for any number n, the parallel definition in terms of n-adic EA′s is equivalent. This proof at one stage uses the deep result of Godei that plus and times form a sub-basis for the recursively enumerable attributes (sets and relations)2. The aim of this note is to prove this equivalence in more pedestrian fashion.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 2 , June 1963 , pp. 161 - 163
Copyright
Copyright © Association for Symbolic Logic 1964

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Footnotes

1

I am indebted to the referee, who suggested using a construction from Smullyan [2] that made my proof shorter and more elegant.

References

[1]Smullyan, R. M., Theory of formal systems, Annals of mathematics studies, no. 47 (1961).CrossRefGoogle Scholar
[2]Smullyan, R. M., Extended canonical systems, Proceedings of the American Mathematicae Society, vol. 12 (1961).Google Scholar