Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T06:26:19.239Z Has data issue: false hasContentIssue false

Metarecursively enumerable sets and their metadegrees

Published online by Cambridge University Press:  12 March 2014

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

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
Copyright
Copyright © Association for Symbolic Logic 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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. 236238.CrossRefGoogle ScholarPubMed
[2]Friedberg, R. M., Three theorems on recursive enumeration, this Journal, vol. 23 (1958), pp. 309316.Google Scholar
[3]Kreisel, G. and Sacks, G. E., Metarecursive sets, this Journal, vol. 30 (1965), pp. 318338.Google Scholar
[4]Sacks, G. E., A maximal set which is not complete, Michigan Mathematical Journal, vol. 11 (1964), pp. 193205.CrossRefGoogle Scholar
[5]Sacks, G. E., The recursively enumerable degrees are dense, Annals of Mathematics, vol. 80 (1964), pp. 300312.CrossRefGoogle Scholar
[6]Sacks, G. E., Metarecursively enumerable sets and admissible ordinals, Bulletin of the American Mathematical Society, vol. 72 (1966), pp. 5964.CrossRefGoogle Scholar
[7]Yates, C. E. M., Three theorems on the degrees of recursively enumerable sets, Duke Mathematical Journal, vol. 32 (1965), pp. 461468.CrossRefGoogle Scholar