Publications

  1. Natural large degree spectra, with D. Diamondstone and D. Turetsky, submitted.
  2. Characterising lowness for Demuth randomness, with L. Bienvenu, R. Downey, A. Nies, and D. Turetsky, submitted.
  3. Galvin's "racing pawns" game, internal hyperarithmetic comprehension, and the law of excluded middle, with C. Conidis and D. Turetsky, submitted.
  4. Relative to any non-hyperarithmetic set, with A. Montalbán and T.A. Slaman, submitted.
  5. Inherent enumerability of strong jump-traceability, with D. Diamondstone and D. Turetsky, submitted.
  6. Computability and uncountable linear orderings, with A. Kach, S. Lempp, and D. Turetsky, submitted.
  7. Pseudo-jump inversion and SJT-hard sets, with R. Downey, submitted.
  8. Strong jump-traceability and Demuth randomness, with D. Turetsky, submitted.
  9. Anti-complexity, lowness and highness notions, and reducibilities with tiny use, with J. Franklin, F. Stephan and G. Wu, submitted.
  10. Martin-Löf random points satisfy Birkhoff's ergodic theorem with respect to effectively closed sets, with J. Franklin, J. Miller, and K.M. Ng, to appear in the Proceedings of the American Mathematical Society.
  11. Computable structure theory using admissible recursion theory on ω1, with J. Knight, to appear in Greenberg, Hamkins, Hirschfeldt and Miller (eds.), Effective Mathematics of the Uncountable, Lecture Notes in Logic, ASL, Cambridge.
  12. Strong jump-traceability II: K-triviality, with R. Downey, to appear in the Israel Journal of Mathematics.
  13. Characterising the strongly jump-traceable sets via randomness, with D. Hirschfeldt and A. Nies, submitted.
    (This is a slightly expanded version.)
  14. The Slaman-Wehner theorem in higher recursion theory, with A. Montalbán and T.A. Slaman.
    Proceedings of the American Mathematical Society 139 (2011), pp. 1865-1869.
  15. K-trivial sets are never continuously random, with G. Barmpalias, A. Montalbán, and T.A. Slaman.
    In Arai et. al. (eds.), Proceedings of the 11th Asian Logic Conference, Singapore, World Scientific (2011), pp. 51-58.
  16. A random set which only computes strongly jump-traceable c.e. sets.
    Journal of Symbolic Logic 76 (2011), pp. 700-718.
  17. Extensions of embeddings below computably enumerable degrees, with R. Downey, A.E.M. Lewis, and A. Montalbán, to appear in Transactions of the American Mathematical Society.
  18. Binary subtrees with few labelled paths, with R. Downey, C. Jockusch, and K. Milans.
    Combinatorica 31 (2011), pp. 285-303.
  19. Diagonally non-recursive functions and effective Hausdorff dimension, with J. Miller.
    Bulletin of the London Mathematical Society 43 (2011), pp. 636-654.
  20. Benign cost functions and lowness notions, with A. Nies.
    Journal of Symbolic Logic 76 (2011), pp. 289-312.
  21. Lowness for Kurtz randomness, with J. Miller.
    Journal of Symbolic Logic 74 (2009), pp. 665-678.
  22. K-trivial degrees and the jump-traceability hierarchy, with G. Barmpalias and R. Downey.
    Proceedings of the American Mathematical Society 137 (2009), pp. 2099-2109.
  23. Working with strong reducibilities above totally ω-c.e. and array computable degrees, with G. Barmpalias and R. Downey.
    Transactions of the American Mathematical Society 362 (2010), pp. 777-813.
  24. Turing degrees of reals of positive packing dimension, with R. Downey.
    Information Processing Letters 108 (2008), pp. 198-203.
  25. The upward closure of a perfect thin class, with R. Downey and J. Miller.
    Annals of Pure and Applied Logic 156 (2008), pp. 51-58.
  26. Strong jump-traceability I: the computably enumerable case, with R. Downey and P. Cholak.
    Advances in Mathematics 217 (2008), pp. 2045-2074.
  27. Totally <ωω-computably enumerable degrees and m-topped degrees, with R. Downey.
    In Cai, Cooper, Li (eds.), Theory and Applications of Models of Computation (proceedings of TAMC 2006, Beijing), Lecture Notes in Computer Science 3959, Springer (2006), pp. 46-60.
  28. Totally ω-computably enumerable degrees and bounding critical triples, with R. Downey and R. Weber.
    Journal of Mathematical Logic 7 (2007), pp. 145-171.
  29. Models of real-valued measurability, with S. Fuchino and S. Shelah.
    Annals of Pure and Applied Logic 142 (2006), pp. 380-397.
  30. Lowness for computable machines, with R. Downey, A. Nies and N. Mihailović.
    In Chong et. al. (eds.), Computational Prospects of Infinity, Lecture Notes Series of the Institute for Mathematical Sciences, NUS, vol. 15, World Scientific (2008), pp. 79-86.
  31. Every 1-generic computes a properly 1-generic, with B. Csima, R. Downey, D. Hirschfeldt, and J. Miller.
    Journal of Symbolic Logic 71 (2006), pp. 1385-1393.
  32. Prompt simplicity, array computability, and cupping, with R. Downey, J. Miller and R. Weber.
    In Chong et. al. (eds.), Computational Prospects of Infinity, Lecture Notes Series of the Institute for Mathematical Sciences, NUS, vol. 15, World Scientific (2008), pp. 59-78.
  33. Uniform almost everywhere domination, with P. Cholak and J. Miller.
    Journal of Symbolic Logic 71 (2006), pp. 1057-1072.
  34. Ranked structures and arithmetic transfinite recursion, with A. Montalbán.
    Transactions of the American Mathematical Society 360 (2008), 1265-1307.
  35. The role of true finiteness in the admissible recursively enumerable degrees.
    Bulletin of Symbolic Logic 11 3 (2005), pp. 398-410.
  36. The role of true finiteness in the admissible recursively enumerable degrees.
    Memoirs of the American Mathematical Society 181 854 (2006), 99 pages.
  37. Embedding and coding below a 1-generic degree, with A. Montalbán.
    Notre Dame Journal of Formal Logic 44 (2003), pp. 200-216.
  38. Generalized high degrees have the complementation property, with A. Montalbán and R.A. Shore.
    Journal of Symbolic Logic 69 (2004), pp. 1200-1220.
  39. The elementary theory of the metarecursively enumerable degrees, with T.A. Slaman and R.A. Shore.
    Journal of Mathematical Logic 6 (2006), pp. 380-397.