Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

 

 

Metarecursively enumerable sets and admissible ordinals


Author: Gerald E. Sacks
Journal: Bull. Amer. Math. Soc. 72 (1966), 59-64
MathSciNet review: 0215707
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. J. C. E. Dekker, A theorem on hypersimple sets, Proc. Amer. Math. Soc. 5 (1954), 791–796. MR 0063995, 10.1090/S0002-9939-1954-0063995-6
  • 2. G. Driscoll, Contributions to metarecursion theory, Ph.D. Thesis, Cornell University, Ithaca, N. Y., 1965.
  • 3. 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 0084474
  • 4. Richard M. Friedberg, Three theorems on recursive enumeration. I. Decomposition. II. Maximal set. III. Enumeration without duplication, J. Symb. Logic 23 (1958), 309–316. MR 0109125
  • 5. Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790
  • 6. S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals. II, Amer. J. Math. 77 (1955), 405–428. MR 0070595
  • 7. 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
  • 8. G. Kreisel and Gerald E. Sacks, Metarecursive sets, J. Symbolic Logic 30 (1965), 318–338. MR 0213233
  • 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).
  • 15. Gerald E. Sacks, On the degrees less than 0′, Ann. of Math. (2) 77 (1963), 211–231. MR 0146078
  • 16. Clifford Spector, Recursive well-orderings, J. Symb. Logic 20 (1955), 151–163. MR 0074347


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1966-11416-7