Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

$ \mathrm{wtt}$-complete sets are not necessarily $ \mathrm{tt}$-complete


Author: A. H. Lachlan
Journal: Proc. Amer. Math. Soc. 48 (1975), 429-434
DOI: https://doi.org/10.1090/S0002-9939-1975-0357087-X
MathSciNet review: 0357087
Full-text PDF

Abstract | References | Additional Information

Abstract: A recursively enumerable set is constructed which is complete with respect to weak truth-table reducibility but not with respect to truth-table reducibility. In contrast it is also shown that, when bounded weak truth-table reducibility is defined in the natural way, completeness with respect to this reducibility is the same as that with respect to bounded truth-table reducibility.


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

  • [1] R. M. Friedberg and H.Rogers, Jr., Reducibility and completeness for sets of integers, Z. Math. Logik Grundlagen Math. 5 (1959), 117-125. MR 22 #3682. MR 0112831 (22:3682)
  • [2] A. H. Lachlan, Some notions of reducibility and productiveness, Z. Math. Logik Grundlagen Math. 11 (1965), 17-44. MR 30 #3014. MR 0172795 (30:3014)
  • [3] -, A note on universal sets, J. Symbolic Logic 31 (1966), 573-574. MR 35 #2732. MR 0211857 (35:2732)
  • [4] R. E. Ladner and L. P. Sasso, Jr., The weak truth-table degrees of recursively enumerable sets (preprint).
  • [5] D. A. Martin, Completeness, the recursion theorem, and effectively simple sets, Proc. Amer. Math. Soc. 17 (1966), 838-842. MR 36 #45. MR 0216950 (36:45)
  • [6] E. L. Post, Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc. 50 (1944), 284-316. MR 6, 29. MR 0010514 (6:29f)
  • [7] H. Rogers, Jr. Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967. MR 37 #61. MR 0224462 (37:61)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0357087-X
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society