- Semirecursive sets and positive reducibility,
*Trans. Amer. Math. Soc.*131 (1968), 420-436. - Supplement to Boone's "Algebraic systems", in
*Contributions to Mathematical Logic*, edited by K. Schütte, Wiley-Interscience, New York, NY, 1968, 34-36. - Uniformly introreducible sets,
*J. Symbolic Logic*33 (1968), 521-536. - The degrees of bi-immune sets,
*Z. Math. Logik Grundlagen Math.*15 (1969), 135-140. - Countable retracing functions and P
^{0}_{2}predicates (with T. G. McLaughlin),*Pacific J. Math.*30 (1969), 67-93. - Relationships between reducibilities,
*Trans. Amer. Math. Soc.*142 (1969), 229-237. - The degrees of hyperhyperimmune sets,
*J. Symbolic Logic*34 (1969), 489-493. - Minimal covers and arithmetical sets (with Robert I. Soare),
*Proc. Amer. Math. Soc.*25 (1970), 856-859. - A minimal pair of P
^{0}_{1}classes (with Robert I. Soare),*J. Symbolic Logic*36 (1971), 66-78. - P
^{0}_{1}classes and degrees of theories (with Robert I. Soare),*Trans. Amer. Math. Soc.*173 (1972), 33-56. - Degrees of members of P
^{0}_{1}classes (with Robert I. Soare),*Pacific J. Math.*40 (1972), 605-616. - Ramsey's theorem and recursion theory,
*J. Symbolic Logic*37 (1972), 268-280. - A reducibility arising from the Boone groups,
*Mathematica Scandinavica*31 (1972), 262-266. - Upward closure of bi-immune degrees,
*Z. Math. Logik Grundlagen Math.*18 (1972), 285-287. - Degrees in which the recursive sets are uniformly recursive,
*Canad. J. Math.*24 (1972), 1092-1099. - An application of sum^0_4 determinacy to the degrees of unsolvability,
*J. Symbolic Logic*38 (1973), 293-294. - Encodability of Kleene's O (with Robert I. Soare),
*J. Symbolic Logic*38 (1973), 437-440. - Upward closure and cohesive degrees,
*Israel J. Math.*15 (1973), 332-335. - Post's problem and his hypersimple set (with Robert I. Soare),
*J. Symbolic Logic*38 (1973), 446-452. - P
^{0}_{1}classes and Boolean combinations of recursively enumerable sets,*J. Symbolic Logic*39 (1974), 95-96. - Recursiveness of initial segments of Kleene's O,
*Fund. Math.*87 (1975), 161-167. - A lattice property of Post's simple set (with P. F. Cohen),
*Illinois J. Math.*19 (1975), 450-453. - A degree theoretic definition of the ramified analytical hierarchy (with S. G. Simpson),
*Ann. Math. Logic*10 (1975), 1-32. - Completely autoreducible degrees (with M. Paterson),
*Z. Math. Logik Grundlagen Math.*22 (1976), 571-575. - First order topology (with C. W. Henson, L. A. Rubel, and G. Takeuti),
*Dissertationes Math.*143 (1977), 5-40. - Fixed points of jump preserving automorphisms of degrees (with R. M. Solovay),
*Israel J. Math.*26 (1977), 91-94. - Simple proofs of some theorems on high degrees,
*Canad. J. Math.*29 (1977), 1072-1080. - Double jumps of minimal degrees (with D. B. Posner),
*J. Symbolic Logic*43 (1978), 715-724. - Fine degrees of word problems of cancellation semigroups,
*Z. Math. Logik, Grundlagen Math.*26 (1980), 93-95. - 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.
- 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.
- Automorphism bases for degrees of unsolvability (with D. B. Posner),
*Israel J. Math.*40 (1981), 150-164. - Pseudo jump operators I: the r.e. case (with R. A. Shore),
*Trans. Amer. Math. Soc.*275 (1983), 599-609. - 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. - 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. - 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.
- Pseudo-jump operators II: Transfinite iterations, hierarchies, and minimal covers (with R. A. Shore),
*J. Symbolic Logic*49 (1984), 1205-1236. - 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.
- Embedding the diamond lattice in the recursively enumerable truth-table degrees (with J. Mohrherr),
*Proc. Amer. Math. Soc.*94 (1985), 123-128. - 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.
- T-degrees, jump classes, and strong reducibilities (with R. G. Downey),
*Trans. Amer. Math. Soc.*301(1987), 103-136. - 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. - 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.
- Jumps of orderings (with C. J. Ash and J. F. Knight),
*Trans. Amer. Math. Soc.*319 (1990), 573-599. - 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.
- Weakly semirecursive sets (with J. C. Owings),
*J. Symbolic Logic*55 (1990), 637-644. - Degrees of isomorphic copies of linear orderings (with R. I. Soare),
*Annals of Pure and Applied Logic*52 (1991), 39-64. - P
^{0}_{1}classes and Rado's selection principle (with A. Lewis and J. B. Remmel),*J. Symbolic Logic*56 (1991), 684-693. - On the S
_{2}-theory of the upper semilattice of Turing degrees (with T. Slaman),*J. Symbolic Logic*58 (1993), 193-204. - 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. - Countable thin P
^{0}_{1}classes (with D. Cenzer, R. Downey, and R. Shore),*Annals of Pure and Applied Logic*59 (1993), 79-139. - 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.
- Every low Boolean algebra is isomorphic to a recursive one (with R. Downey),
*Proc. Amer. Math. Soc.*122 (1994), 871-880. - Boolean algebras, Stone spaces, and the iterated Turing jump (with R. Soare),
*J. Symbolic Logic*59 (1994), 1121-1138. - Weak presentations of computable fields (with A. Shlapentokh),
*J. Symbolic Logic*60 (1995), 199-208. - Difference sets and inverting the difference operator (with L. Rubel and Z. Füredi),
*Combinatorica,*16 (1996), 87-106. - 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. - Difference sets and computability theory (with R. Downey, L. Rubel, and Z. Füredi),
*Annals of Pure and Applied Logic*93 (1998), 63-72. - Effective presentability of Boolean algebras of Cantor-Bendixson rank 1 (with R. Downey),
*J. Symbolic Logic*64 (1999), 45-52. - Generalized cohesiveness (with Tamara Hummel),
*J. Symbolic Logic*64 (1999), 489-516. - 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.) - P
^{0}_{1}classes - Structure and applications (with D. Cenzer),*Contemporary Mathematics*257 (2000), 39-59. - Ramsey's theorem for computably enumerable colorings (with
T. Hummel),
*Journal of Symbolic Logic*66 (2001), 873-880. - Generalized r-cohesiveness and the arithmetical hierarchy: A
correction to "Generalized cohesiveness" (with T. Lakins),
*J. Symbolic Logic*67 (2002), 1078-1082. - 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. - A join theorem for the computably enumerable degrees (with A.
Li and Y. Yang),
*Trans. Amer. Math. Soc.*, 356 (2004), 2557-2568. - Completing pseudojump operators (with R. Coles, R. Downey, and G.
LaForte),
*Annals of Pure and Applied Logic*136 (2005), 297-333. - On self-embeddings of computable linear orderings (with R. Downey
and J. Miller),
*Annals of Pure and Applied Logic*138 (2006), 52-76. - 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. - Restricted jump interpolation in the dce degrees, (with Angsheng
Li),
*Mathematical Structures in Computer Science*, Vol. 16, issue 05, Oct. 2006, pp 841-865. - 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. - Chains and antichains in partial orderings (with Valentina
Harizanov and Julia Knight),
*Archive for Mathematical Logic*48 (2009), 39-53. - Ramsey's theorem and cone avoidance (with Damir Dzhafarov),
*J. Symbolic Logic*74 (2) (2009), 557-578. - Stability and posets (with Bart Kastermans, Steffen Lempp,
Manuel Lerman, and Reed Solomon),
*J. Symbolic Logic*74 (2) (2009), 693-711. - Binary subtrees with few labeled paths (with Rod Downey, Noam
Greenberg, and Kevin Milans),
*Combinatorica*31 (3) (2011), 285-303. - Generic computability, Turing degrees, and asymptotic density
(with Paul Schupp),
*Journal of the London Mathematical Society*85 (2) (2012), 472-490. - Asymptotic density and computably enumerable sets
(with Rod Downey and Paul Schupp),
*J. Mathematical Logic*13 (3) (2013). - Diagonally non-computable functions and bi-immunity (with Andrew E. M. Lewis),
*J. Symbolic Logic*78 (3), 977-988. - Asymptotic density and the Ershov hierarchy (with Rod Downey, Timothy H. McNicholl, and Paul Schupp),
*Mathematical Logic Quarterly.*61 (2015), 189-195 - Asymptotic density, computable traceability and 1-randomness (with
Uri Andrews, Mingzhong Cai, David Diamondstone, and Steffen Lempp),
*Fundamenta Mathematicae*234 (2016), 41-53. - Asymptotic density and the coarse computability bound (with
Denis Hirschfeldt, Timothy McNicholl, and Paul Schupp),
*Computability*5 (2016), 13-27. - Coarse reducibility and algorithmic randomness (with
Denis Hirschfeldt, Rutger Kuyper, and Paul Schupp),
to appear in
*J. Symbolic Logic*. - On notions of computability theoretic reductions between $\Pi^1_2$
principles (with Denis Hirschfeldt),
*Journal of Mathematical Logic*6, Issue 01 (2016), 1650002 (59 pages). - Herrmann's beautiful theorem on computable partial orderings,
to appear in
*Computability and Complexity*, edited by Adam Day, Michael Fellows, Noam Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer, to be published in 2017. - Effectiveness of Hindman's theorem for bounded sums (with Damir
Dzhafarov, Reed Solomon, and Linda Brown Westrick), to appear in
*Computability and Complexity*, edited by Adam Day, Michael Fellows, Noam Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer, to be published in 2017. - Asymptotic density and the theory of computability : A partial
survey (with Paul Schupp), to appear in
*Computability and Complexity*, edited by Adam Day, Michael Fellows, Noam Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer, to be published in 2017.

*Last modified August 12, 2016.*