Publications by Carl G. Jockusch

  1. Semirecursive sets and positive reducibility, Trans. Amer. Math. Soc. 131 (1968), 420-436.
  2. Supplement to Boone's "Algebraic systems", in Contributions to Mathematical Logic, edited by K. Schütte, Wiley-Interscience, New York, NY, 1968, 34-36.
  3. Uniformly introreducible sets, J. Symbolic Logic 33 (1968), 521-536.
  4. The degrees of bi-immune sets, Z. Math. Logik Grundlagen Math. 15 (1969), 135-140.
  5. Countable retracing functions and P02 predicates (with T. G. McLaughlin), Pacific J. Math. 30 (1969), 67-93.
  6. Relationships between reducibilities, Trans. Amer. Math. Soc. 142 (1969), 229-237.
  7. The degrees of hyperhyperimmune sets, J. Symbolic Logic 34 (1969), 489-493.
  8. Minimal covers and arithmetical sets (with Robert I. Soare), Proc. Amer. Math. Soc. 25 (1970), 856-859.
  9. A minimal pair of P01 classes (with Robert I. Soare), J. Symbolic Logic 36 (1971), 66-78.
  10. P01 classes and degrees of theories (with Robert I. Soare), Trans. Amer. Math. Soc. 173 (1972), 33-56.
  11. Degrees of members of P01 classes (with Robert I. Soare), Pacific J. Math. 40 (1972), 605-616.
  12. Ramsey's theorem and recursion theory, J. Symbolic Logic 37 (1972), 268-280.
  13. A reducibility arising from the Boone groups, Mathematica Scandinavica 31 (1972), 262-266.
  14. Upward closure of bi-immune degrees, Z. Math. Logik Grundlagen Math. 18 (1972), 285-287.
  15. Degrees in which the recursive sets are uniformly recursive, Canad. J. Math. 24 (1972), 1092-1099.
  16. An application of sum^0_4 determinacy to the degrees of unsolvability, J. Symbolic Logic 38 (1973), 293-294.
  17. Encodability of Kleene's O (with Robert I. Soare), J. Symbolic Logic 38 (1973), 437-440.
  18. Upward closure and cohesive degrees, Israel J. Math. 15 (1973), 332-335.
  19. Post's problem and his hypersimple set (with Robert I. Soare), J. Symbolic Logic 38 (1973), 446-452.
  20. P01 classes and Boolean combinations of recursively enumerable sets, J. Symbolic Logic 39 (1974), 95-96.
  21. Recursiveness of initial segments of Kleene's O, Fund. Math. 87 (1975), 161-167.
  22. A lattice property of Post's simple set (with P. F. Cohen), Illinois J. Math. 19 (1975), 450-453.
  23. A degree theoretic definition of the ramified analytical hierarchy (with S. G. Simpson), Ann. Math. Logic 10 (1975), 1-32.
  24. Completely autoreducible degrees (with M. Paterson), Z. Math. Logik Grundlagen Math. 22 (1976), 571-575.
  25. First order topology (with C. W. Henson, L. A. Rubel, and G. Takeuti), Dissertationes Math. 143 (1977), 5-40.
  26. Fixed points of jump preserving automorphisms of degrees (with R. M. Solovay), Israel J. Math. 26 (1977), 91-94.
  27. Simple proofs of some theorems on high degrees, Canad. J. Math. 29 (1977), 1072-1080.
  28. Double jumps of minimal degrees (with D. B. Posner), J. Symbolic Logic 43 (1978), 715-724.
  29. Fine degrees of word problems of cancellation semigroups, Z. Math. Logik, Grundlagen Math. 26 (1980), 93-95.
  30. Degrees of generic sets, in Recursion Theory: its Generalisations and Applications, edited by F. R. Drake and S. S. Wainer, Cambridge University Press, 1980, pp. 110-139.
  31. Three easy constructions of recursively enumerable sets, pp. 83-91 in Logic Year 1979-80 (Lecture Notes in Math, v. 859), edited by M. Lerman, J. H. Schmerl, and R. I. Soare, (Springer Verlag, Berlin, Heidelberg, New York, 1981), 83-91.
  32. Automorphism bases for degrees of unsolvability (with D. B. Posner), Israel J. Math. 40 (1981), 150-164.
  33. Pseudo jump operators I: the r.e. case (with R. A. Shore), Trans. Amer. Math. Soc. 275 (1983), 599-609.
  34. An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees (with K. Ambos-Spies, R. Shore, and R. Soare), Trans. Amer. Math. Soc. 281 (1984), 109-128.
  35. Recursively enumerable sets and van der Waerden's theorem on arithmetic progressions (with I. Kalantari), Pacific J. Math. 36. Minimal degrees and 1-generic sets below 0 (with C. T. Chong), in Computation and Proof Theory, Proceedings, Logic Colloquium Aachen 1983, Part II, edited by M. M. Richter, E. Börger, W. Oberschelp, B. Schinzel and W. Thomas, Lecture Notes in Mathematics, Vol. 1104, Springer Verlag, Berlin, Heidelberg, New York, Tokyo, 1984, 63-77.
  36. Minimal degrees and 1-generic sets below f 0 (with C. T. Chong), in Computation and Proof Theory, Proceedings, Logic Colloquium Aachen 1983, Part II, edited by M. M. Richter, E. Börger, W. Oberschelp, B. Schinzel and W. Thomas, Lecture Notes in Mathematics, Vol. 1104, Springer Verlag, Berlin, Heidelberg, New York, Tokyo, 1984, 63-77.
  37. Pseudo-jump operators II: Transfinite iterations, hierarchies, and minimal covers (with R. A. Shore), J. Symbolic Logic 49 (1984), 1205-1236.
  38. REA operators, r.e. degrees, and minimal covers, (with R. Shore), in Recursion Theory, edited by A. Nerode and R. Shore, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence, 1985, 3-11.
  39. Embedding the diamond lattice in the recursively enumerable truth-table degrees (with J. Mohrherr), Proc. Amer. Math. Soc. 94 (1985), 123-128.
  40. Genericity for recursively enumerable sets, in Recursion Theory Week (Proceedings, Oberwolfach 1984, Lecture Notes in Mathematics, Vol. 1141) edited by H.-D. Ebbinghaus, G. H. Müller, and G. E. Sacks, Springer Verlag, Berlin, Heidelberg, New York, 1985, 203-232.
  41. T-degrees, jump classes, and strong reducibilities (with R. G. Downey), Trans. Amer. Math. Soc. 301(1987), 103-136.
  42. Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion (with M. Lerman, R. Soare, and R. Solovay), J. Symbolic Logic 54 (1989), 1288-1323.
  43. Degrees of functions with no fixed points, in Logic, Methodology, and Philosophy of Science VIII, edited by J. E. Fenstad, I. T. Frolov, and R. Hilpinen, North-Holland, Amsterdam, New York, Oxford, Tokyo, 1989, 191-201.
  44. Jumps of orderings (with C. J. Ash and J. F. Knight), Trans. Amer. Math. Soc. 319 (1990), 573-599.
  45. Array nonrecursive sets and multiple permitting arguments (with R. G. Downey and M. Stob), in Recursion Theory Week, Proceedings. 1989, edited by K. Ambos-Spies, G. H. Müller, and G. E. Sacks, Lecture Notes in Mathematics, Vol. 1432, Springer-Verlag, Berlin, Heidelberg, Tokyo, New York, 1990, 141-173.
  46. Weakly semirecursive sets (with J. C. Owings), J. Symbolic Logic 55 (1990), 637-644.
  47. Degrees of isomorphic copies of linear orderings (with R. I. Soare), Annals of Pure and Applied Logic 52 (1991), 39-64.
  48. P01 classes and Rado's selection principle (with A. Lewis and J. B. Remmel), J. Symbolic Logic 56 (1991), 684-693.
  49. On the S2-theory of the upper semilattice of Turing degrees (with T. Slaman), J. Symbolic Logic 58 (1993), 193-204.
  50. Decidability and undecidability of theories with a predicate for the primes (with P. T. Bateman and A. Woods), J. Symbolic Logic 58 (1993), 672-687.
  51. Countable thin P01 classes (with D. Cenzer, R. Downey, and R. Shore), Annals of Pure and Applied Logic 59 (1993), 79-139.
  52. A cohesive set which is not high (with Frank Stephan), Mathematical Logic Quarterly 39 (1993), 515-530. (A corrective note keeping the main results intact) appeared in the same journal, Vol. 43 (1997) page 569.
  53. Every low Boolean algebra is isomorphic to a recursive one (with R. Downey), Proc. Amer. Math. Soc. 122 (1994), 871-880.
  54. Boolean algebras, Stone spaces, and the iterated Turing jump (with R. Soare), J. Symbolic Logic 59 (1994), 1121-1138.
  55. Weak presentations of computable fields (with A. Shlapentokh), J. Symbolic Logic 60 (1995), 199-208.
  56. Difference sets and inverting the difference operator (with L. Rubel and Z. Füredi), Combinatorica, 16 (1996), 87-106.
  57. Array nonrecursive sets and genericity (with R. Downey and M. Stob), Computability, Enumerability, Unsolvability: Directions in Recursion Theory, Eds. S. B. Cooper, T. A. Slaman, S. S. Wainer, London Mathematical Society Lecture Notes Series, Cambridge University Press, 1996, 93-104.
  58. Difference sets and computability theory (with R. Downey, L. Rubel, and Z. Füredi), Annals of Pure and Applied Logic 93 (1998), 63-72.
  59. Effective presentability of Boolean algebras of Cantor-Bendixson rank 1 (with R. Downey), J. Symbolic Logic 64 (1999), 45-52.
  60. Generalized cohesiveness (with Tamara Hummel), J. Symbolic Logic 64 (1999), 489-516.
  61. On the strength of Ramsey's theorem for pairs (with P. Cholak and T. Slaman), Journal of Symbolic Logic 66 (2001) 1-55. (A corrective note appeared in the same journal (Vol. 74 (4) (2009), 1438-1439. This note corrects several proofs but keeps all results intact.)
  62. P01 classes - Structure and applications (with D. Cenzer), Contemporary Mathematics 257 (2000), 39-59.
  63. Ramsey's theorem for computably enumerable colorings (with T. Hummel), Journal of Symbolic Logic 66 (2001), 873-880.
  64. Generalized r-cohesiveness and the arithmetical hierarchy: A correction to "Generalized cohesiveness" (with T. Lakins), J. Symbolic Logic 67 (2002), 1078-1082.
  65. Free sets and reverse mathematics (with P. Cholak, M. Giusto, and J. Hirst), pp. 104-119 in Reverse Mathematics 2001, edited by Stephen G. Simpson, Lecture Notes in Logic, Association for Symbolic Logic, 2005.
  66. A join theorem for the computably enumerable degrees (with A. Li and Y. Yang), Trans. Amer. Math. Soc., 356 (2004), 2557-2568.
  67. Completing pseudojump operators (with R. Coles, R. Downey, and G. LaForte), Annals of Pure and Applied Logic 136 (2005), 297-333.
  68. On self-embeddings of computable linear orderings (with R. Downey and J. Miller), Annals of Pure and Applied Logic 138 (2006), 52-76.
  69. The strength of some combinatorial principles related to Ramsey's theorem for pairs, (with D. Hirschfeldt, B. Kjos-Hanssen, S. Lempp, and T. Slaman), pp. 143-161 in Proceedings of the Program on Computational Prospects of Infinity, edited by C.T. Chong, Qi Feng, Theodore Slaman, Hugh Woodin, and Yue Yang, Vol. 15 in the Lecture Note Series of the Institute for Mathematical Sciences, National University of Singapore, World Scientific, New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai, 2008.
  70. Restricted jump interpolation in the dce degrees, (with Angsheng Li), Mathematical Structures in Computer Science , Vol. 16, issue 05, Oct. 2006, pp 841-865.
  71. Strong degree sprectra of relations and Pi-0-1 classes, (with John Chisholm, Jennifer Chubb, Valentina Harizanov, Timothy McNicholl, and Sarah Pingrey), J. Symbolic Logic 72 (2007), 1003-1018.
  72. Chains and antichains in partial orderings (with Valentina Harizanov and Julia Knight), Archive for Mathematical Logic 48 (2009), 39-53.
  73. Ramsey's theorem and cone avoidance (with Damir Dzhafarov), J. Symbolic Logic 74 (2) (2009), 557-578.
  74. Stability and posets (with Bart Kastermans, Steffen Lempp, Manuel Lerman, and Reed Solomon), J. Symbolic Logic 74 (2) (2009), 693-711.
  75. Binary subtrees with few labeled paths (with Rod Downey, Noam Greenberg, and Kevin Milans), Combinatorica 31 (3) (2011), 285-303.
  76. Generic computability, Turing degrees, and asymptotic density (with Paul Schupp), Journal of the London Mathematical Society 85 (2) (2012), 472-490.
  77. Asymptotic density and computably enumerable sets (with Rod Downey and Paul Schupp), J. Mathematical Logic 13 (3) (2013).
  78. Diagonally non-computable functions and bi-immunity (with Andrew E. M. Lewis), J. Symbolic Logic 78 (3), 977-988.
  79. Asymptotic density and the Ershov hierarchy (with Rod Downey, Timothy H. McNicholl, and Paul Schupp), to appear in Mathematical Logic Quarterly.
  80. Asymptotic density, computable traceability and 1-randomness (with Uri Andrews, Mingzhong Cai, David Diamondstone, and Steffen Lempp), to appear in Fundamenta Mathematicae .
  81. Asymptotic density and the coarse computability bound (with Denis Hirschfeldt, Timothy McNicholl, and Paul Schupp), to appear in Computability .
  82. Coarse reducibility and algorithmic randomness (with Denis Hirschfeldt, Rutger Kuyper, and Paul Schupp), to appear in J. Symbolic Logic .
  83. On notions of computability theoretic reductions between $\Pi^1_2$ principles (with Denis Hirschfeldt), submitted for publication.

Last modified September 14, 2015.