Adam R. Day

Senior Lecturer in Mathematics, Victoria University of Wellington



  1. Jump operations for Borel graphs, with Andrew Marks to appear in Journal of Symbolic Logic, arXiv:1604.02228.
  2. On the Strength of Two Recurrence Theorems, Journal of Symbolic Logic, Volume 81, Number 4 (2016): 1357-1374, journal, arXiv:1305.5858.
  3. Density, forcing and the covering problem, with Joseph S. Miller, Mathematical Research Letters, Volume 22, Number 3, (2015): 719-727), journal, arXiv:1304.2789.
  4. The typical Turing degree, with George Barmpalias and Andrew Lewis, Proceedings of the London Mathematical Society, Volume 109, Number 1 (2014), journal, arXiv:1111.1064.
  5. Computing K-Trivial Sets by Incomplete Random Sets, with Laurent Bienvenu, Noam Greenberg, Antonín Kučera, Joseph S. Miller, André Nies, Dan Turetsky, Bulletin of Symbolic Logic, Volume 20, Number 1 (2014) arXiv:1305.5514.
  6. Cupping with random sets, with Joseph S. Miller, Proceedings of the American Mathematical Society, Volume 142 (2014) journal, arXiv:1206.1603.
  7. Algorithmic independence and PA degrees, with Jan Reimann, Notre Dame Journal of Formal Logic, Volume 55, Number 1 (2014) 1-10, journal, arXiv:1207.2533.
  8. Randomness for non-computable measures, with Joseph S. Miller, Transactions of the American Mathematical Society,Vol 365, no. 7 (2013) 3575-3591 journal, pdf.
  9. From Bi-immunity to Absolute Undecidability, with Laurent Bienvenu and Rupert Hölzl, Journal for Symbolic Logic, Volume 78, Issue 4 (2013), 1025-1346 journal, arXiv:1210.4937.
  10. Limits to joining with generics and randoms, with Damir Dzhafarov, in R. Downey, J. Brendle, R. Goldblatt, and B. Kim (editors), Proceedings of the 12th Asian Logic Conference, World Scientific, (2013), 76-88 arXiv:1209.3282.
  11. Indifferent sets for genericity, Journal for Symbolic Logic, Volume 78, Issue 1 (2013), 113-138 journal, pdf.
  12. Process and truth-table characterizations of randomness, Theoretical Computer Science, Vol 452, (2012), Pages 47-55, journal, pdf.
  13. A constructive version of Birkhoff’s ergodic theorem for Martin-Löf random points with Laurent Bienvenu, Mathieu Hoyrup, Ilya Mezhirov, and Alexander Shen, Information and Computation, Vol 210, (2012), Pages 21–30, journal, arXiv:1007.5249.
  14. Increasing the gap between descriptional complexity and algorithmic probability, Transactions of the American Mathematical Society, Vol 363, no. 10, (2011), Pages 5577-5604. A conference version of this paper appeared in CCC ’09: Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, 2009, Pages 263-273, journal, pdf.
  15. The Computable Lipschitz Degrees of Computably Enumerable Sets are not Dense, Annals of Pure and Applied Logic, Vol 161, Issue 12, (2010), Pages 1588-1602, journal, pdf.
  16. On Process Complexity, Chicago Journal of Theoretical Computer Science, Vol 2010, Issue 4, (2010). An initial version of this paper was presented at CATS 2009: Fifteenth Computing: The Australasian Theory Symposium, journal (open access).
  17. On the Computational Power of Random Strings, Annals of Pure and Applied Logic, Vol 160, Issue 2, (2009), Pages 214-228, journal, pdf.

PhD thesis

Randomness and computability, pdf.