Pacific Journal of Mathematics

Degrees of members of $\Pi^0_1$ classes.

Carl G. Jockusch, Jr. and Robert I. Soare

Article information

Source
Pacific J. Math., Volume 40, Number 3 (1972), 605-616.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102968559

Mathematical Reviews number (MathSciNet)
MR0309722

Zentralblatt MATH identifier
0209.02201

Subjects
Primary: 02F40

Citation

Jockusch, Carl G.; Soare, Robert I. Degrees of members of $\Pi^0_1$ classes. Pacific J. Math. 40 (1972), no. 3, 605--616. https://projecteuclid.org/euclid.pjm/1102968559


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References

  • [1] P. J. Cohen, Set theory and the continuum hypothesis, W. A. Benjamin, New York 1966.
  • [2] C. G. Jockusch, Jr., A new proof of Martin'scharacterizationof the degrees of maximal sets, unpublished.
  • [3] C. G. Jockusch and T. G. McLaughlin, Countable retracing functionsand Tl2 pre- dicates, Pacific J. Math., 30 (1969), 67-93.
  • [4] C. G. Jockusch and R. I. Soare, j classes and degrees of theories to appear in Trans. Amer. Math. Soc.
  • [5] A. H. Lachlan, Lower bounds forpairs of recursively enumerable degrees, Proc. London Math. Soc. 16 (1966), 537-569.
  • [6] D. A. Martin, Completeness, the recursion theorem, and effectively simple sets, Proc. Amer. Math. Soc, 17 (1966), 838-842.
  • [7] D. A. Martin, Classes of r.e. sets and degrees of unsolvability, Z. Math. Logik Grundlagen Math. 12 (1966), 295-310.
  • [8] E. L. Post, Recursively enumerable sets of integers and their decision problems, Bull. Amer, Math. Soc, 50 (1944), 284-316.
  • [9] H. Rogers, Theory of recursive functionsand effective computability, McGraw-Hill, New York, 1967.
  • [10] G. E. Sacks, A minimal degree less than 0', Bull. Amer. Math. Soc, 67 (1961), 416-419.
  • [11] G. E. Sacks, Degrees of unsolvability, Ann. of Math. Studies No. 55, Princeton Univ. Press, Princeton, N. J., 1963.
  • [12] D. Scott, Algebras of sets binumerable in complete extensions of arithmetic,Pro- ceedings of Symposium in Pure Mathematics, vol. V, Recursive Function Theory, 117- 121, Amer, Math. Soc Providence, R, I., 1962.
  • [13] D. Scott and S. Tennenbaum, On the degrees of complete extensions ofarithmetic, Notices Amer. Math. Soc, 7 (1960), 242-243.
  • [14] J. R. Shoenfield, Degrees of models, J. Symbolic Logic, 25 (1960), 233-237.
  • [5] J. R. Shoenfield, On degrees of unsolvability, Ann. of Math., (2) 69 (1959), 644-653.
  • [16] J. R. Shoenfield, The class of recursive functions, Proc Amer. Math. Soc, 9 (1958), 690- 692.
  • [17] R. M. Smullyan, Effectively simple sets, Proc. Amer. Math. Soc, 15 (1964), 893- 895.
  • [18] R. I. Soare, The Friedberg-Muchnik theorem re-examined, to appear in Canad. J. Math.
  • [19] C. E. M. Yates, Recursively enumerable degrees and the degrees less than O', in Sets, Models, and Recursion Theory, North Holland Publishing Company, Amsterdam, 1967. 264-271.
  • [20] C. E. M. Yates, Three theorems on the degrees of recursively enumerable sets, Duke Math. J., 32 (1965), 461-468.