Johanna N.Y. Franklin

Publications

Published/Accepted

  1. omega-change randomness and weak Demuth randomness (with Keng Meng Ng) (.pdf)
    To appear in the Journal of Symbolic Logic.

  2. Lowness for difference tests (with David Diamondstone) (.pdf)
    To appear in the Notre Dame Journal of Formal Logic.

  3. Anti-complex sets and reducibilities with tiny use (with Noam Greenberg, Frank Stephan, and Guohua Wu) (.pdf)
    Journal of Symbolic Logic, vol. 78 (2013), pp. 1307-1327.

  4. Local computability for ordinals (with Asher M. Kach, Russell Miller, and Reed Solomon) (.pdf)
    In P. Bonizzoni, V. Brattka, and B. Loewe, eds., Lecture Notes in Computer Science, vol. 7921 (2013), pp. 161-170.

  5. Degrees of categoricity and the hyperarithmetic hierarchy (with Barbara F. Csima and Richard A. Shore) (.pdf)
    Notre Dame Journal of Formal Logic, vol. 54 (2013), pp. 215-231.

  6. Martin-Loef random points satisfy Birkhoff's ergodic theorem for effectively closed sets (with Noam Greenberg, Joseph S. Miller, and Keng Meng Ng) (.pdf)
    Proceedings of the AMS, vol. 140 (2012), pp. 3623-3628.

  7. Relativizations of randomness and genericity notions (with Frank Stephan and Liang Yu) (.pdf)
    Bulletin of the London Mathematical Society, vol. 43 (2011), pp. 721-733.

  8. Van Lambalgen's Theorem and high degrees (with Frank Stephan) (.pdf)
    Notre Dame Journal of Formal Logic, vol. 52 (2011), pp. 173-185.

  9. A superhigh diamond in the c.e. tt-degrees (with Douglas Cenzer, Jiang Liu, and Guohua Wu) (.pdf)
    Archive for Mathematical Logic, vol. 50 (2011), pp. 33-44.

  10. Difference randomness (with Keng Meng Ng) (.pdf)
    Proceedings of the AMS, vol. 139 (2011), pp. 345-360.

  11. Subclasses of the weakly random reals (.pdf)
    Notre Dame Journal of Formal Logic, vol. 51 (2010), pp. 417-426.

  12. Schnorr trivial sets and truth-table reducibility (with Frank Stephan) (.pdf)
    Journal of Symbolic Logic, vol. 75 (2010), pp. 501-521.
    An earlier version was published as Technical Report TRA3/08, School of Computing, National University of Singapore, 2008.

  13. Schnorr triviality and genericity (.pdf)
    Journal of Symbolic Logic, vol. 75 (2010), pp. 191-207.

  14. Lowness and highness properties for randomness notions (survey paper) (.pdf)
    In T. Arai et al., editors, Proceedings of the 10th Asian Logic Conference, pp. 124-151. World Scientific, 2010.

  15. Hyperimmune-free degrees and Schnorr triviality (.pdf)
    Journal of Symbolic Logic, vol. 73 (2008), pp. 999-1008.

  16. Schnorr trivial reals: A construction (.pdf)
    Archive for Mathematical Logic, vol. 46 (2008), pp. 665-678.
    An earlier version appeared in Electronic Notes in Theoretical Computer Science, 167 (2007), pp. 79-93.

Submitted

  1. Randomness and nonergodic systems (with Henry Towsner) (.pdf)

  2. Degrees that are low for isomorphism (with Reed Solomon) (.pdf)

In preparation

  1. On intersections of r.e. and random sets (with Frank Stephan)

  2. The Turing degrees of UD-random reals (with Wesley Calvert)

  3. LR-bases and their Turing degrees (with Keng Meng Ng and Reed Solomon)

Other

  1. Six papers on lowness and highness for randomness notions
    Bulletin of Symbolic Logic. vol. 19(1) (2013), pp. 115-118.

  2. Greg Chaitin: Mathematics, Biology, and Metabiology
    Fields Notes, vol. 10(2) (2010), p. 8.