Research

Interests | Papers

Interests

My mathematical interests include effective dimension, randomness, effective algebra and computability theory.

I describe some of my work, using only the 1000 most common English words.

Papers

  1. Finding Bases of Free Abelian Groups is Usually Difficult

    With Noam Greenberg and Linda Brown Westrick.

    Submitted.

  2. Computability-Theoretic Categoricity and Scott Families

    With Ekaterina Fokina and Valentina Harizanov.

    Submitted.

  3. The Finite Intersection Principle and Genericity

    With David Diamondstone, Rod Downey and Noam Greenberg.

    To appear in the Mathematical Proceedings of the Cambridge Philosophical Society.

  4. Two More Characterizations of K-Triviality

    With Noam Greenberg, Joe Miller and Benoit Monin.

    To appear in the Notre Dame Journal of Formal Logic.

  5. Coherent Randomness Tests and Computing The K-trivial Sets

    With Laurent Bienvenu, Noam Greenberg, Antonín Kučera and André Nies.

    To appear in the Journal of the European Mathematical Society.

  6. Linear Orders Realized by c.e. Equivalence Relations

    With Ekaterina Fokina, Bakhadyr Khoussainov and Pavel Semukhin.

    To appear in the Journal of Symbolic Logic.

  7. The Complexity of Computable Categoricity

    With Rod Downey, Asher Kach, Steffen Lempp, Andy Lewis and Antonio Montalbán.

    Advances in Mathematics 268 (2015), pp. 423-466.

  8. Index Sets for n-Decidable Structures Categorical Relative to m-Decidable Presentations

    With Ekaterina Fokina, Sergei Goncharov, Valentina Harizanov and Oleg Kudinov.

    Algebra and Logic 54:4 (2015), pp. 336-341.

  9. Partial Functions and Domination

    With C.T. Chong, Gordon Hoi and Frank Stephan.

    Logical Methods in Computer Science 11 (2015), 3:16.

  10. Computability and Uncountable Linear Orderings I: Computable Categoricity

    With Noam Greenberg, Asher Kach and Steffen Lempp.

    Journal of Symbolic Logic 80:1 (2015), pp. 116-144.

  11. Computability and Uncountable Linear Orderings II: Degree Spectra

    With Noam Greenberg, Asher Kach and Steffen Lempp.

    Journal of Symbolic Logic 80:1 (2015), pp. 145-178.

  12. Lowness for Effective Hausdorff Dimension

    With Steffen Lempp, Joe Miller, Selwyn Ng and Rebecca Weber.

    Journal of Mathematical Logic 14:2 (2015).

  13. Inherent Enumerability of Strong Jump Traceability

    With David Diamondstone and Noam Greenberg.

    Transactions of the American Mathematical Society 367 (2015), pp. 1771-1796.

  14. Characterizing Lowness for Demuth Randomness

    With Laurent Bienvenu, Rod Downey, Noam Greenberg and Andre Nies.

    Journal of Symbolic Logic 79:2 (2014), pp. 526-560.

  15. Strong Jump Traceability and Demuth Randomness

    With Noam Greenberg.

    Proceedings of the London Mathematical Society, 108 (2014), 738-779.

  16. Joining Non-Low C.E. Sets with Diagonally Non-Computable Functions

    With Laurent Bienvenu, Noam Greenberg, Antonín Kučera, Joe Miller and André Nies.

    Journal of Logic and Computation, 23 (2013), 1183-1194.

  17. A Van Lambalgen Theorem for Demuth Randomness

    With David Diamondstone and Noam Greenberg.

    Proceedings of the 12th Asian Logic Colloquium, Wellington, World Scientific (2013), pp. 115-124.

  18. Computable Categoricity Versus Relative Computable Categoricity

    With Rod Downey, Asher Kach and Steffen Lempp.

    Fundamenta Mathematicae, 221:2 (2013), 129-159.

  19. Galvin's "Racing Pawns" Game, Internal Hyperarithmetic Comprehension, and the Law of Excluded Middle

    With Chris Conidis and Noam Greenberg.

    Notre Dame Journal of Formal Logic, 54:2 (2013), 233-252.

  20. Natural Large Degree Spectra

    With David Diamondstone and Noam Greenberg.

    Computability, 1 (2012), 99-106.

  21. A K-trivial Set Which Is Not Jump Traceable At Certain Orders

    Information Processing Letters, 112 (2012), 544-547

  22. Limitwise Monotonic Functions and Applications

    With Rod Downey and Asher Kach.

    Proceedings of the Asian Logic Conference, 2011, 59-85.

  23. Connectedness Properties of Dimension Level Sets

    Theoretical Computer Science, 412 (2011), 3598-3603

  24. Limitwise Monotonic Functions, Sets and Degrees on Computable Domains

    With Asher Kach.

    Journal of Symbolic Logic, 75:1 (2010), 131-154

  25. Decidability and Computability of Certain Torsion-Free Abelian Groups

    With Rod Downey, Sergei Goncharov, Asher Kach, Julia Knight, Oleg Kudinov and Alexander Melnikov.

    Notre Dame Journal of Formal Logic, 51:1 (2010), 85-96.

  26. Δ02-Categoricity of Equivalence Structures

    With Asher Kach.

    New Zealand Journal of Mathematics, 39 (2009), 143-149.

  27. Π11 Equivalence Relations and Hyperarithmetic Isomorphism

    With Noam Greenberg.

    In preparation.

  28. High Sets Computable from every SJT-Hard Set

    With David Diamondstone, Rod Downey and Noam Greenberg.

    In preparation.

  29. The Computability of Uncountable Linear Orders and the Cantor‐Bendixson Derivative

    With David Diamondstone and Noam Greenberg.

    In preparation.