Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Metarecursively enumerable sets and admissible ordinals
HTML articles powered by AMS MathViewer

by Gerald E. Sacks PDF
Bull. Amer. Math. Soc. 72 (1966), 59-64
References
  • J. C. E. Dekker, A theorem on hypersimple sets, Proc. Amer. Math. Soc. 5 (1954), 791–796. MR 63995, DOI 10.1090/S0002-9939-1954-0063995-6
  • 2. G. Driscoll, Contributions to metarecursion theory, Ph.D. Thesis, Cornell University, Ithaca, N. Y., 1965.
  • Richard M. Friedberg, Two recursively enumerable sets of incomparable degrees of unsolvability (solution of Post’s problem, 1944), Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 236–238. MR 84474, DOI 10.1073/pnas.43.2.236
  • Richard M. Friedberg, Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication, J. Symbolic Logic 23 (1958), 309–316. MR 109125, DOI 10.2307/2964290
  • Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790
  • S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals. II, Amer. J. Math. 77 (1955), 405–428. MR 70595, DOI 10.2307/2372632
  • G. Kreisel, Model-theoretic invariants: Applications to recursive and hyperarithmetic operations, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 190–205. MR 0199107
  • G. Kreisel and Gerald E. Sacks, Metarecursive sets, J. Symbolic Logic 30 (1965), 318–338. MR 213233, DOI 10.2307/2269621
  • 9. S. Kripke, Transfinite recursions on admissible ordinals I (Abstract), J. Symbolic Logic 29 (1964), 161. 10. S. Kripke, Transfinite recursions on admissible ordinals II (Abstract), J. Symbolic Logic 29 (1964), 161-162. 11. S. Kripke, Admissible ordinals and the analytic hierarchy, (Abstract), J. Symbolic Logic 29 (1964), 162. 12. A. A. Muchnik, Negative answer to the problem of reducibility of the theory of algorithms, Dokl. Akad. Nauk SSSR 108 (1956), 144-197. 13. G. E. Sacks, Post’s problem, admissible ordinals, and regularity, (to appear). 14. G. E. Sacks, Axioms for recursion theory, (in preparation).
  • Gerald E. Sacks, On the degrees less than 0′, Ann. of Math. (2) 77 (1963), 211–231. MR 146078, DOI 10.2307/1970214
  • Clifford Spector, Recursive well-orderings, J. Symbolic Logic 20 (1955), 151–163. MR 74347, DOI 10.2307/2266902
Additional Information
  • Journal: Bull. Amer. Math. Soc. 72 (1966), 59-64
  • DOI: https://doi.org/10.1090/S0002-9904-1966-11416-7
  • MathSciNet review: 0215707