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Real numbers and functions in the Kleene hierarchy and limits of recursive, rational functions

Published online by Cambridge University Press:  12 March 2014

N. Z. Shapiro
N. Z. Shapiro*
Affiliation:
The Rand Corporation
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Extract

Let ƒ be a real number. It is well known [7] that the set of rational numbers which are less than ƒ is a recursive set if and only if ƒ is representable as the limit of a recursive, recursively convergent sequence of rational numbers. In this paper we replace the condition that the set of rational numbers less than ƒ is recursive by the condition that this set is at various points in the Kleene hierarchy, and we replace the recursive, recursively convergent limit by a variety of other recursive limiting processes.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 2 , 25 July 1969 , pp. 207 - 214
Copyright
Copyright © Association for Symbolic Logic 1969

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References

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