Journal Publications

  1. Computability up to homeomorphism (with Matthew Harrison-Trainor and Alexander Melnikov).
  2. Submitted.



  3. Martingales and restricted ratio betting (with Sumedh Masulkar and Satyadev Nandakumar).
  4. Submitted.



  5. Foundations of online structure theory II: The operator approach (with Rod Downey and Alexander Melnikov).
  6. Submitted.



  7. Cupping and jump classes in the computably enumerable degrees, Part I: Highness (with Noam Greenberg and Guohua Wu).
  8. Submitted.



  9. Online presentations of finitely generated structures (with Nikolay Bazhenov, Iskander Kalimullin and Alexander Melnikov).
  10. Submitted.



  11. Minimal degrees and downwards density in some strong s-reducibilities and Q-reducibilities (with Irakli Chitaia, Andrea Sorbi and Yue Yang).
  12. Submitted.



  13. Multiple genericity (with Michael McInerney).
  14. Submitted.



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



  17. A structure of punctual dimension two (with Alexander Melnikov).
  18. Proceedings of the American Mathematical Society. Accepted.



  19. Computable linear orders and products (with Andrey Frolov, Steffen Lempp and Guohua Wu).
  20. Journal of Symbolic Logic. Accepted.



  21. Enumerating abelian p-groups (with Rod Downey and Alexander Melnikov).
  22. Journal of Algebra. Accepted.



  23. Incomparability in local structures of s-degrees and Q-degrees (with Irakli Chitaia, Andrea Sorbi and Yue Yang).
  24. Archive for Mathematical Logic, To appear.



  25. Effective domination and the bounded jump (with Hongyuan Yu).
  26. Notre Dame Journal of Formal Logic. To appear.



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



  29. Turing degrees in Polish spaces and decomposability of Borel functions (with Vassilios Gregoriades and Takayuki Kihara).
  30. Journal of Mathematical Logic, To appear.



  31. On Kierstead's Conjecture (with Maxim Zubkov).
  32. Transactions of the American Mathematical Society (2019), 372(5), pp. 3713-3753.



  33. Categorical linearly ordered structures (with Rod Downey and Alexander Melnikov).



  34. Automatic and polynomial-time algebraic structures (with Nikolay Bazhenov, Matthew Harrison-Trainor, Iskander Kalimullin and Alexander Melnikov).
  35. Journal of Symbolic Logic (2019), 84(4), pp. 1630-1669.



  36. The back-and-forth method and computability without delay (with Alexander Melnikov).
  37. Israel Journal of Mathematics (2019), 234(2), pp. 959-1000.



  38. On the degree structure of equivalence relations under computable reducibility (with Hongyuan Yu).
  39. Notre Dame Journal of Formal Logic (2019), 60(4), pp. 733-761.



  40. Computable torsion abelian groups (with Alexander Melnikov).
  41. Advances in Mathematics (2018), 325, pp. 864907.



  42. Splitting into degrees with low computational strength (with Rod Downey).
  43. Annals of Pure and Applied Logic (2018), 169(8), pp. 803-834.



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

  46. Lowness and logical depth (with Rod Downey and Michael McInerney).
  47. Theoretical Computer Science (2017), 702, pp. 23-33.



  48. A Friedberg enumeration of equivalence structures (with Rod Downey and Alexander Melnikov).
  49. Journal of Mathematical Logic, (2017), 17, 1750008.



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



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



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



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



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



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

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



  64. Counting the changes of random Δ2 sets (with Santiago Figueira, Denis Hirschfeldt, Joseph S. Miller and Andre Nies).
  65. Journal of Logic and Computation (2015), 25(4), pp 1073-1089. doi:10.1093/logcom/exs083



  66. Efficiency and robustness of different bus network designs (with Zhen Fu Pang, Bin Othman Nasri and Christopher Monterola.).
  67. International Journal of Modern Physics C (2015), 26(3).

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



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



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



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



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



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



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



  81. 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.



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



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



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



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



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



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



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



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



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



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



Conference Proceedings

  1. Computability and categoricity of weakly homogeneous Boolean algebras and p-groups (with Douglas Cenzer and Francis Adams).
  2. Submitted.



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



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



  7. The computational aspects of hyperimmunefree degrees (with Frank Stephan, Yang Yue and Yu Liang).
  8. Proceedings of the 12th Asian Logic Conference (2012), pp. 271-284. doi:10.1142/9789814449274_0015



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



  11. Counting the changes of random Δ2 sets (with Santiago Figueira, Denis Hirschfeldt, Joseph S. Miller and Andre Nies).
  12. Computability in Europe 2010, pp. 162-171.



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



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



  17. A cuppable nonbounding degree.
  18. 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.