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Metarecursively enumerable sets and their metadegrees

Published online by Cambridge University Press:  12 March 2014

Graham C. Driscoll Jr
Graham C. Driscoll Jr*
Affiliation:
International Business Machines Corp.
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Extract

Metarecursion theory is an analogue of recursion theory which deals with sets of recursive, or constructive, ordinals rather than of natural numbers. It was originated by Kreisel and Sacks [3], who make extensive use of an equation calculus developed by Kripke. We assume that the reader is acquainted with the outline of it given in [3], and especially in [3, §3].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 3 , 10 October 1968 , pp. 389 - 411
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Friedberg, R. M., Two recursively enumerable sets of incomparable degrees of unsolvability, Proceedings of the National Academy of Sciences of the U.S.A., vol. 43 (1957), pp. 236–238.CrossRefGoogle ScholarPubMed
[2]Friedberg, R. M., Three theorems on recursive enumeration, this Journal, vol. 23 (1958), pp. 309–316.Google Scholar
[3]Kreisel, G. and Sacks, G. E., Metarecursive sets, this Journal, vol. 30 (1965), pp. 318–338.Google Scholar
[4]Sacks, G. E., A maximal set which is not complete, Michigan Mathematical Journal, vol. 11 (1964), pp. 193–205.CrossRefGoogle Scholar
[5]Sacks, G. E., The recursively enumerable degrees are dense, Annals of Mathematics, vol. 80 (1964), pp. 300–312.CrossRefGoogle Scholar
[6]Sacks, G. E., Metarecursively enumerable sets and admissible ordinals, Bulletin of the American Mathematical Society, vol. 72 (1966), pp. 59–64.CrossRefGoogle Scholar
[7]Yates, C. E. M., Three theorems on the degrees of recursively enumerable sets, Duke Mathematical Journal, vol. 32 (1965), pp. 461–468.CrossRefGoogle Scholar