Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T03:05:41.583Z Has data issue: false hasContentIssue false
  • English
  • Français

Splinters of recursive functions1

Published online by Cambridge University Press:  12 March 2014

J. S. Ullian
J. S. Ullian*
Affiliation:
Johns Hopkins University
Get access Rights & Permissions [Opens in a new window]

Extract

Basic notation in this paper is as in [3]. From [5] and [9] the following additional notation is derived, ϕi is the partial recursive function with index i, Wi its range. ∅ is the empty set. ‘≡’ denotes isomorphism between sets, ‘≡m’ many-one equivalence, ‘≡T’ Turing equivalence, ‘≦1’ and ‘≦m’ signify one-one and many-one reducibility respectively. ‘Recursive’ is used throughout for ‘general recursive’.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 25 , Issue 1 , March 1960 , pp. 33 - 38
Copyright
Copyright © Association for Symbolic Logic 1960

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.)

Footnotes

1

Adapted from a doctoral thesis in the Department of Philosophy of Harvard University. I am indebted to Professors W. V. Quine and Burton S. Dreben of Harvard for their guidance and encouragement, and to Professor Hartley Rogers, Jr., of the Massachusetts Institute of Technology for his important suggestions.

References

[1]Dekker, J. C. E., Two notes on recursively enumerable sets, Proceedings of the American Mathematical Society, vol. 4 (1953), pp. 495–501.CrossRefGoogle Scholar
[2]Hermes, H., Zum Begriff der Axiomatisierbarkeit, Mathematische Nachrichten, vol. 4 (1950–1951), pp. 343–347.CrossRefGoogle Scholar
[3]Kleene, S. C., Introduction to metamathematics, Amsterdam (North Holland), Groningen (Noordhoff), New York and Toronto (Van Nostrand) 1952, x + 550 pp.Google Scholar
[4]Kleene, S. C., Finite axiomatizability of theories in the predicate calculus using additional predicate symbols, Memoirs of the American Mathematical Society, no. 10 (Two papers on the predicate calculus), Providence, 1952, pp. 27–68.Google Scholar
[5]Myhill, J., Creative sets, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 1 (1955), pp. 97–108.CrossRefGoogle Scholar
[6]Myhill, J. and Dekker, J. C. E., Recursive functions, forthcoming.Google Scholar
[7]Post, E. L., Recursively enumerable sets of positive integers and their decision problems, Bulletin of the American Mathematical Society, vol. 50 (1944), pp. 284–316.CrossRefGoogle Scholar
[8]Quine, W. V., Mathematical logic, revised edition, Cambridge (Harvard), 1951, xii + 346 pp.CrossRefGoogle Scholar
[9]Rogers, H. Jr., Theory of recursive functions and effective computability, vol. I (mimeographed by Massachusetts Institute of Technology, 1956).Google Scholar