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.
- Richard M. Friedberg and Hartley Rogers Jr., Reducibility and completeness for sets of integers, Z. Math. Logik Grundlagen Math. 5 (1959), 117–125. MR 112831, DOI 10.1002/malq.19590050703
- A. H. Lachlan, Some notions of reducibility and productiveness, Z. Math. Logik Grundlagen Math. 11 (1965), 17–44. MR 172795, DOI 10.1002/malq.19650110104
- A. H. Lachlan, A note on universal sets, J. Symbolic Logic 31 (1966), 573–574. MR 211857, DOI 10.2307/2269692 R. E. Ladner and L. P. Sasso, Jr., The weak truth-table degrees of recursively enumerable sets (preprint).
- Donald A. Martin, Completeness, the recursion theorem, and effectively simple sets, Proc. Amer. Math. Soc. 17 (1966), 838–842. MR 216950, DOI 10.1090/S0002-9939-1966-0216950-5
- Emil L. Post, Recursively enumerable sets of positive integers and their decision problems, Bull. Amer. Math. Soc. 50 (1944), 284–316. MR 10514, DOI 10.1090/S0002-9904-1944-08111-1
- Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 429-434
- DOI: https://doi.org/10.1090/S0002-9939-1975-0357087-X
- MathSciNet review: 0357087