Publications

  1. Multiple genericity (with Michael McInerney).
  2. Submitted.



  3. Computable torsion abelian groups (with Alexander Melnikov).
  4. Submitted.



  5. Splitting into degrees with low computational strength (with Rod Downey).
  6. Submitted.



  7. The diversity of categoricity without delay (with Iskander Kalimullin and Alexander Melnikov).
  8. Algebra and Logic (2017), 56(2), pp. 256266.

  9. Lowness and logical depth (with Rod Downey and Michael McInerney).
  10. Theoretical Computer Science. To appear.



  11. Minimal weak truth table degrees and computably enumerable Turing degrees (with Rod Downey and Reed Solomon).
  12. Memoirs of the American Mathematical Society. To appear.



  13. A Friedberg enumeration of equivalence structures (with Rod Downey and Alexander Melnikov).
  14. Journal of Mathematical Logic. To appear.



  15. Optimal depth-first algorithms and equilibria of independent distributions on multi-branching trees (with Weiguang Peng, Ningning Peng, Kazayuki Tanaka and Yue Yang).
  16. Information Processing Letters (2017), 125, pp. 41-45.



  17. Turing degrees in Polish spaces and decomposability of Borel functions (with Vassilios Gregoriades and Takayuki Kihara).
  18. Submitted.



  19. Algebraic structures computable without delay (with Iskander Kalimullin and Alexander Melnikov).
  20. Theoretical Computer Science (2017), 674, pp. 7398.



  21. A normal form theorem on computable functions over real numbers (with Nazanin R. Tavana and Yue Yang).
  22. Submitted.



  23. Abelian p-groups and the Halting problem (with Rod Downey and Alexander Melnikov).
  24. Annals of Pure and Applied Logic (2016), 167(11), pp.1123-1138.



  25. On Δ02-categoricity of equivalence relations (with Rod Downey and Alexander Melnikov).
  26. Annals of Pure and Applied Logic (2015), 166(9), pp. 851-880.



  27. Lowness for effective Hausdorff dimension (with Steffen Lempp, Joseph Miller, Daniel Turetsky and Rebecca Weber).
  28. Journal of Mathematical Logic (2014), 14(2)



  29. Finitary reducibilities on equivalence relations (with Russell Miller).
  30. Journal of Symbolic Logic (2016), 81(4), pp. 1225-1254.



  31. Computably enumerable Turing degrees and the meet property (with Benedict Durrant, Andy Lewis-Pye and James Riley).
  32. Proceedings of the American Mathematical Society (2016), 144(4), pp. 1735-1744.



  33. An analogy between cardinal characteristics and highness properties of oracles (with Joerg Brendle, Andrew Brooke-Taylor and Andre Nies).
  34. Proceedings of the 13th Asian Logic Conference (2015), pp. 1-29.



  35. Minimal pairs in the r.e. truth table degrees (with Rod Downey).
  36. Proceedings of the 13th Asian Logic Conference (2015), pp. 53-68.



  37. Iterated effective embeddings of abelian p-groups (with Rod Downey and Alexander Melnikov).
  38. International Journal of Algebra and Computation (2014), 24(7), pp.1055-1084.



  39. Complexity of equivalence relations and preorders from computability theory (with Egor Ianofski, Russell Miller and Andre Nies).
  40. Journal of Symbolic Logic (2014), 79(3), pp. 859-881.



  41. Computable structures and operations on the space of continuous functions (with Alexander Melnikov).
  42. Fundamenta Mathematicae (2016), 233(2), pp.101-141.

  43. The computational aspects of hyperimmunefree degrees (with Frank Stephan, Yang Yue and Yu Liang).


  44. The complexity of recursive splittings of random sets (with Andre Nies and Frank Stephan).
  45. Computability (2014), 3(1), pp. 1-8.



  46. ω-change randomness and weak Demuth randomness (with Johanna Franklin).
  47. Journal of Symbolic Logic (2014), 79(3), pp. 776-791.



  48. Universal computably enumerable equivalence relations (with Uri Andrews, Steffen Lempp, Joseph Miller, Luca San Mauro and Andrea Sorbi).



  49. Lowness for bounded randomness (with Rod Downey).
  50. Theoretical Computer Science (2012), 460C, pp. 1-9. doi:10.1016/j.tcs.2012.06.004.



  51. Bounded randomness (with Paul Brodhead and Rod Downey).
  52. M.J. Dinneen et al. (Eds.): Workshop on Theoretical Computer Science 2012 (Calude Festschrift), LNCS 7160, pp. 59--70. Springer, Heidelberg (2012)



  53. Martin-Lof random points satisfy Birkhoff's ergodic theorem for effectively closed sets (with Johanna N.Y. Franklin, Noam Greenberg and Joseph S. Miller).
    Proceedings of the American Mathematical Society (2012), 140(10), pp. 3623-3628.



  54. Limits on jump inversion for strong reducibilities (with Barbara Csima and Rod Downey).
  55. Journal of Symbolic Logic (2011), 76(4), pp. 1287-1296.



  56. Difference randomness (with Johanna N.Y. Franklin).
  57. Proceedings of the American Mathematical Society (2011), 139, pp. 345-360.



  58. Strengthening prompt simplicity (with David Diamondstone).
  59. Journal of Symbolic Logic (2011), 76(3), pp. 946-972.



  60. Jump inversions inside effectively closed sets and applications to randomness (with Rod Downey and George Barmpalias).
  61. Journal of Symbolic Logic (2011), 76(2), pp. 491-518.



  62. Beyond strong jump traceability.
  63. Proceedings of the London Mathematical Society (2011), 102(3), pp. 423-467.



  64. Counting the changes of random Δ2 sets (with Santiago Figueira, Denis Hirschfeldt, Joseph S. Miller and Andre Nies).



  65. Effective packing dimension and traceability (with Rod Downey).
  66. Notre Dame Journal of Formal Logic (2010), 51(2), pp. 279-290.



  67. The importance of Π01 classes in effective randomness (with George Barmpalias and Andy Lewis).
  68. Journal of Symbolic Logic (2010), 75(1), pp. 387-400.



  69. Lowness for Demuth Randomness (with Rod Downey).
  70. Mathematical Theory and Computational Practice, Lecture Notes in Computer Science (2009), 5635, pp. 154-166.



  71. On the degrees of diagonal sets and the failure of the analogue of a theorem of Martin.
  72. Notre Dame Journal of Formal Logic (2009), 50(4), pp. 469-493.



  73. On strongly jump traceable reals.
  74. Annals of Pure and Applied Logic (2008), 154, pp. 51-69.



  75. On very high degrees.
  76. Journal of Symbolic Logic (2008), 73(1), pp. 309-342.



  77. Degrees of weakly computable reals (with Frank Stephan and Guohua Wu).
  78. Proceedings of "Second Conference on Computability in Europe", CiE 2006, Swansea (2006), pp. 413-422.



  79. A cuppable nonbounding degree.
  80. Computational prospects of infinity. Part II. Presented talks, 207--223, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 15, World Sci. Publ., Hackensack, NJ, 2008.



Papers in preparation

  1. Cupping Ahmad pairs (with Iskander Kalimullin, Steffen Lempp and Mars Yamaleev).

  2. On one point extension in the &Sigma02 enumeration degrees (with Uri Andrews, Steffen Lempp and Andrea Sorbi).

  3. Contiguity and strong contiguity (with Mars Yamaleev).

  4. Strong jump traceability and almost superdeepness (with David Diamondstone).

  5. On the c.e. degrees which can be realized in a Π01 class (with Barbara Csima and Rod Downey).

  6. The computational aspects of hyperimmunefree degrees (with Frank Stephan, Yang Yue and Yu Liang).

  7. Cupping and the High/Low hierarchy (with Noam Greenberg and Guohua Wu).

  8. A superhigh minimal Turing degree (with Steffen Lempp and Joe Miller).

  9. Two properties of ultrahigh degrees (with Jiang Liu).