## Publications

### Books

- Revolutions and Revelations in Computability (co-edited with Ulrich Berger, Florin Manea, and Arno Pauly). Springer, Lecture Notes in Computer Science, vol. 13359, 2022.

- Algorithmic Randomness: Progress and Prospects (co-edited with Christopher P. Porter). Cambridge University Press, Lecture Notes in Logic, vol. 50, 2020.

### Published/Accepted articles

- Structural highness notions (with Wesley Calvert and Dan Turetsky) (arXiv)

*Journal of Symbolic Logic*, to appear.

- A Church-Turing Thesis for Randomness? (.pdf, typo on second page corrected from published version)

In L. De Mol, A. Weiermann, F. Manea, and D. Fernández-Duque, eds., Lecture Notes in Computer Science, vol. 12813, pp. 217-226, 2021.

- Degrees of and lowness for isometric isomorphism (with Timothy H. McNicholl) (arXiv)

*Journal of Logic and Analysis*, vol. 12(6), pp. 1-23, 2020.

- Key developments in algorithmic randomness (survey paper with Christopher P. Porter).

In J. Franklin and C. Porter, eds., Algorithmic Randomness: Progress and Prospects, pp. 1-39. Cambridge University Press, 2020.

- Relativization in randomness (survey paper).

In J. Franklin and C. Porter, eds., Algorithmic Randomness: Progress and Prospects, pp. 134-174. Cambridge University Press, 2020.

- Lowness for isomorphism, countable ideals, and computable traceability (with Reed Solomon) (arXiv)

*Mathematical Logic Quarterly*, vol. 66(1), pp. 104-114, 2020.

- Taking the path computably traveled (with Dan Turetsky) (arXiv)

*Journal of Logic and Computation*, vol. 29(6), pp. 969-973, 2019.

- Algorithmic randomness and Fourier analysis (with Timothy H. McNicholl and Jason Rute) (arXiv)

*Theory of Computing Systems,*vol. 63(3), pp. 567-586, 2019.

- Lowness for isomorphism and degrees of genericity (with Dan Turetsky) (.pdf)

*Computability,*vol. 7(1), pp. 1-6, 2018.

- Strength and weakness in computable structure theory (survey paper) (.pdf)

In A. Day et al., eds.,*Lecture Notes in Computer Science,*vol. 10010, pp. 302-323, 2017.

- Genericity and UD-random reals (with Wesley Calvert) (.pdf)

*Journal of Logic and Analysis,*vol. 7(4), pp. 1-10, 2015.

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

*Moscow Mathematical Journal,*vol. 14, pp. 711-744, 2014.

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

*Computability,*vol. 3, pp. 73-89, 2014.

- omega-change randomness and weak Demuth randomness (with Keng Meng Ng) (.pdf)

*Journal of Symbolic Logic,*vol. 79, pp. 776-791, 2014.

- Lowness for difference tests (with David Diamondstone) (.pdf)

*Notre Dame Journal of Formal Logic,*vol. 55, pp. 63-73, 2014.

- Anti-complex sets and reducibilities with tiny use (with Noam Greenberg, Frank Stephan, and Guohua Wu) (.pdf)

*Journal of Symbolic Logic,*vol. 78, pp. 1307-1327, 2013.

- 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, pp. 161-170, 2013.

- Degrees of categoricity and the hyperarithmetic hierarchy (with Barbara F. Csima and Richard A. Shore) (.pdf)

*Notre Dame Journal of Formal Logic,*vol. 54, pp. 215-231, 2013.

- 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, pp. 3623-3628, 2012.

- Relativizations of randomness and genericity notions (with Frank Stephan and Liang Yu) (.pdf)

*Bulletin of the London Mathematical Society,*vol. 43, pp. 721-733, 2011.

- Van Lambalgen's Theorem and high degrees (with Frank Stephan) (.pdf)

*Notre Dame Journal of Formal Logic,*vol. 52, pp. 173-185, 2011.

- A superhigh diamond in the c.e. tt-degrees (with Douglas Cenzer, Jiang Liu, and Guohua Wu) (.pdf)

*Archive for Mathematical Logic,*vol. 50, pp. 33-44, 2011.

- Difference randomness (with Keng Meng Ng) (.pdf)

*Proceedings of the AMS,*vol. 139, pp. 345-360, 2011.

- Subclasses of the weakly random reals (.pdf)

*Notre Dame Journal of Formal Logic,*vol. 51, pp. 417-426, 2010.

- Schnorr trivial sets and truth-table reducibility (with Frank Stephan) (.pdf)

*Journal of Symbolic Logic,*vol. 75, pp. 501-521, 2010.

An earlier version was published as Technical Report TRA3/08, School of Computing, National University of Singapore, 2008.

- Schnorr triviality and genericity (.pdf)

*Journal of Symbolic Logic,*vol. 75, pp. 191-207, 2010.

- 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.

- Hyperimmune-free degrees and Schnorr triviality (.pdf)

*Journal of Symbolic Logic,*vol. 73, pp. 999-1008, 2008.

- Schnorr trivial reals: A construction (.pdf)

*Archive for Mathematical Logic,*vol. 46, pp. 665-678, 2008.

An earlier version appeared in*Electronic Notes in Theoretical Computer Science,*167 (2007), pp. 79-93.

### Submitted

- Computable classifications of continuous, transducer, and regular functions (with Rupert Hölzl, Alexander Melnikov, Keng Meng Ng, and Daniel Turetsky) (arXiv)

- Free structures and limiting density (with Meng-Che "Turbo" Ho and Julia Knight
) (arXiv)

### In preparation

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

### Other

- Six papers on lowness and highness for randomness notions

*Bulletin of Symbolic Logic.*vol. 19, pp. 115-118, 2013.

- Greg Chaitin: Mathematics, Biology, and Metabiology

*Fields Notes,*vol. 10, p. 8, 2010.