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Recursive real numbers

Published online by Cambridge University Press:  12 March 2014

A. H. Lachlan
A. H. Lachlan*
Affiliation:
Sidney Sussex College, Cambridge University, Cambridge, England
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Extract

The present work was inspired by Mostowski's paper [3] in which he considers classes of sequences of real numbers, and associated sets of primitive recursive real numbers. The present treatment will differ from that of [3] in that we consider the real numbers in (0, ∞), instead of just those in (0, 1), but this will make little difference. In §1 we develop a general theory, and in §2 we show the relation of this theory to the results contained in [3], and to those of other authors.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 1 , March 1963 , pp. 1 - 16
Copyright
Copyright © Association for Symbolic Logic 1964

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References

REFERENCES

[1]Kleene, S. C., Introduction to metatnathematics, Amsterdam and Groningen (North Holland), Groningen (Noordhoff), New York and Toronto (Van Nostrana), X + 550 pp.Google Scholar
[2]Lehman, R. S., On primitive recursive real numbers, Fundamenta mathematicae, vol. 49 (1961), pp. 105–118.CrossRefGoogle Scholar
[3]Mostowski, A., Computable sequences. Fundamenta mathematicae, vol. 44 (1957), pp. 37–51.CrossRefGoogle Scholar
[4]Peter, R., Rekursive Funktionen, Budapest (Akadémiai Kiadó) 1951, 206 pp.Google Scholar
[5]Specker, E., Nicht konstruktiv beweisbare Satte der Analysis, this Journal, vol. 14, pp. 145–158.Google Scholar