Bulletin of the American Mathematical Society

The decision problem for recursively enumerable degrees

J. R. Shoenfield

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 81, Number 6 (1975), 973-977.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183537392

Mathematical Reviews number (MathSciNet)
MR0387035

Zentralblatt MATH identifier
0339.02043

Subjects
Primary: 02F25 02F30

Citation

Shoenfield, J. R. The decision problem for recursively enumerable degrees. Bull. Amer. Math. Soc. 81 (1975), no. 6, 973--977. https://projecteuclid.org/euclid.bams/1183537392


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References

  • 1. R. 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 18, 867.
  • 2. S. C. Kleene and E. L. Post, The upper semi-lattice of degrees of recursive unsolvability, Ann. of Math. (2) 59 (1954), 379-407. MR 15, 772.
  • 3. A. H. Lachlan, The impossibility of finding relative complements for recursively enumerable degrees, J. Symbolic Logic 31 (1966), 434-454. MR 34 #5673.
  • 4. A. H. Lachlan, Lower bounds for pairs of recursively enumerable degrees, Proc. London Math. Soc. (3) 16 (1966), 537-569. MR 34 #4126.
  • 5. A. H. Lachlan, Distributive initial segments of the degrees of unsolvability, Z. Math. Logik Grundlagen Math. 14 (1968), 457-472. MR 38 #5620.
  • 6. A. H. Lachlan, Embedding nondistributive lattices in the recursively enumerable degrees, Conference in Mathematical Logic—London '70, Lecture Notes in Math., vol. 255, Springer-Verlag, New York, 1972, pp. 149-177.
  • 7. A. A. Mučnik, Negative answer to the problem of reducibility of the theory of algorithms, Dokl. Akad. Nauk SSSR 108 (1956), 194-197. (Russian).
  • 8. G. E. Sacks, Degrees of unsolvability, Ann. of Math. Studies, no. 55, Princeton Univ. Press, Princeton, N.J., 1963. MR 32 #4013.
  • 9. J. R. Shoenfield, Applications of model theory to degrees of unsolvability, Theory of Models (Proc. 1963 Internat. Sympos., Berkeley), North-Holland, Amsterdam, 1965, pp. 359-363. MR 34 #53.
  • 10. J. R. Shoenfield, Degrees of unsolvability, North-Holland, Amsterdam, 1971.
  • 11. C. Spector, On degrees of recursive unsolvability, Ann. of Math. (2) 64 (1956), 581-592. MR 18, 552, 1118.
  • 12. S. K. Thomason, Sublattices of the recursively enumerable degrees, Z. Math. Logik Grundlagen Math. 17 (1971), 273-280. MR 45 #8523.
  • 13. C. E. M. Yates, A minimal pair of recursively enumerable degrees, J. Symbolic Logic 31 (1966), 158-168. MR 34 #5677.