Recursive enumerability and the jump operator

Sacks, Gerald E.

doi:10.1090/S0002-9947-1963-0155747-3

Recursive enumerability and the jump operator

Author: Gerald E. Sacks
Journal: Trans. Amer. Math. Soc. 108 (1963), 223-239
MSC: Primary 02.70
DOI: https://doi.org/10.1090/S0002-9947-1963-0155747-3
MathSciNet review: 0155747
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Richard Friedberg, A criterion for completeness of degrees of unsolvability, J. Symbolic Logic 22 (1957), 159–160. MR 98025, DOI https://doi.org/10.2307/2964177
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 https://doi.org/10.1073/pnas.43.2.236
Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790
S. C. Kleene and Emil L. Post, The upper semi-lattice of degrees of recursive unsolvability, Ann. of Math. (2) 59 (1954), 379–407. MR 61078, DOI https://doi.org/10.2307/1969708

A. A. Muchnik, Negative answer to the problem of reducibility of algorithms, Dokl. Akad. Nauk SSSR 108 (1956), 194-197. (Russian)

Gerald E. Sacks, The universality of the recursively enumerable degrees, Abstract No. 60T-14, Notices Amer. Math. Soc. 7 (1960), 996.

J. R. Shoenfield, On degrees of unsolvability, Ann. of Math. (2) 69 (1959), 644–653. MR 105355, DOI https://doi.org/10.2307/1970028
Clifford Spector, On degrees of recursive unsolvability, Ann. of Math. (2) 64 (1956), 581–592. MR 82457, DOI https://doi.org/10.2307/1969604