Publications in Journals
	Elementary differences between the degrees of unsolvability and degrees of compressibility Annals of Pure and Applied Logic (in press) Format: Summary
	Relative randomness and cardinality Notre Dame Journal of Formal Logic (in press) Format: Summary
	K-trivial degrees and the jump-traceability hierarchy with Rod Downey and Noam Greenberg Proceedings of the American Mathematical Society. 137 (2009) no. 6, 2099-2109 Format: Summary
	The Importance of $\Pi^0_1$ Classes in Effective Randomness with A. Lewis and K.-M. Ng Journal of Symbolic Logic. Volume 75, Number 1 (2010) Format: Summary
	Working with strong reducibilities above totally omega-c.e. and array computable degrees with Rod Downey and Noam Greenberg Transactions of the American Mathematical Society. 362 (2010), 777-813. Format: Summary
	Non-Cupping, Measure and Computably Enumerable Splittings with Anthony Morphett Mathematical Structures in Computer Science. vol. 19 (2009) 25-43 Format: Summary
	$\Pi_0^1$ classes, LR degrees and Turing degrees with Andy Lewis and Frank Stephan Annals of Pure and Applied Logic. Volume 156, Issue 1 (2008) pages 21-38 Format: Summary
	$K$-triviality of closed sets and continuous functions with D. Cenzer, J. Remmel and R. Weber Journal of Logic and Computation 19 (2009), no. 1, 3--16 Format: Summary
	Randomness, Lowness and Degrees with Andy Lewis and Mariya Soskova Journal of Symbolic Logic. vol.73, Issue 2, pp. 559-577 (2008) Format: Summary
	Algorithmic Randomness of Closed Sets with Paul Brodhead, Douglas Cenzer, Seyyed Dashti and Rebecca Weber Journal of Logic and Computation 2007 17:1041-1062. Format: Summary
	Algorithmic Randomness of Continuous Functions with P. Brodhead, D. Cenzer, J.B. Remmel and R. Weber Archive for Mathematical Logic, Volume 46, Numbers 7-8, May 2008 Format: Summary
	Post's Programme for the Ershov Hierarchy with Bahareh Afshari, S.~Barry Cooper and Frank Stephan Journal of Logic and Computation 2007 17:1025-1040. Format: Summary
	Randomness and the Linear degrees of computability with Andy Lewis Annals of Pure and Applied Logic Volume 145, Issue 3, (2007), pages 252-257 Format: Summary
	Random Non-Cupping Revisited Journal of Complexity 22 (2006) 850-857. Format: Summary
	The Hypersimple-free c.e. wtt degrees are dense in the c.e. wtt degrees with Andy Lewis Notre Dame Journal of Formal Logic Volume 47 Issue 3 (2006) Format: Summary
	A c.e. real that cannot be sw-computed by any omega number with Andy Lewis Notre Dame Journal of Formal Logic Volume 47 Issue 2 (2006) Format: Summary
	Random Reals and Lipschitz Continuity with Andy Lewis Mathematical Structures in Computer Science Volume 16, issue 5 (2006) Format: Summary
	The $ibT$ Degrees of C.E. Sets are Not Dense with Andy Lewis Annals of Pure and Applied Logic Volume 141, Issues 1-2, 2006 Format: Summary
	Hypersimplicity and Semicomputability in the Weak Truth Table Degrees Archive for Math. Logic Vol.44, Number 8 (2005) 1045 - 1065 Format: Summary
	$h$-Monotonically Computable Real Numbers with X. Zheng and R. Rettinger Mathematical Logic Quarterly, Vol.51 No.2 157-170 (2005) Format: Summary
	Approximation representations for reals and their wtt degrees Mathematical Logic Quarterly Vol. 50 number 4/5 (2004) 370-380 Format: Summary
	Approximation representations for $\Delta_2$ reals Archive for Math. Logic, Volume 43, Number 8, (2004) p. 947 - 964 Format: Summary
	The approximation structure of a computably approximable real J. Symbolic Logic, Vol.68, no.3 (2003) 885--922 Format: Summary
	A transfinite hierarchy of reals Mathematical Logic Quarterly, Vol. 49, Number 2 (2003) 163-172. Format: Summary

	Publications in Conference Volumes
	$K$-trivial closed sets and continuous functions with D. Cenzer, J. Remmel and R. Weber CIE 2007, Computation and Logic in the Real World, Third Conference on Computability in Europe Siena, Italy, June 2007, S.B. Cooper, B. Loewe and A. Sorbi (Eds.) Springer Lecture Notes in Computer Science 4497 (2007), 135-145. Format: Summary
	Working with the LR Degrees with Andy Lewis, Mariya Soskova Theory and Applications of Models of Computation: 4th International Conference TAMC 2007, Shanghai, China, May 2007, Proceedings (J.-Y. Cai, S.B. Cooper, H. Zhu, eds.) Springer Lecture Notes in Computer Science, LNCS 4484, 2007 Format: Summary
	A cappable almost everywhere dominating computably enumerable degree with Antonio Montalban Electronic Notes in Theoretical Computer Science Volume 167 (2007) Format: Summary
	Immunity properties and the n-c.e. hierarchy with Bahareh Afshari and S. Barry Cooper Theory and Applications of Models of Computation Proceedings of the Third Annual Conference on Computation and Logic TAMC06, Beijing, May 2006 (Jin-Yi Cai, S. Barry Cooper, Angsheng Li, eds.) Springer Lecture Notes in Computer Science. Format: Summary
	Computably enumerable sets in the Solovay and the Strong Weak Truth Table Degrees LNCS Volume 3526, proceedings of the CiE conference 2005 conference in Amsterdam (2005) 8-17 Format: Summary
	On the Monotonic Computability of Semi-computable Real Numbers with Xizhong Zheng Lecture Notes in Computer Science, Springer-Verlag, Heidelberg, Volume 2731 / 2003, p.290-300 Format: Summary
	On 0'-computable reals Electronic Notes in Theoretical Computer Science, Vol.66, Issue 1, Eds. V. Brattka, M. Schroder and K. Weihrauch, Elsevier Science Publishers, 2002. Summary

	Recent Papers
	Jump inversions inside effectively closed sets and applications to randomness with Rod Downey and Keng-Meng Ng Submitted. Format: Summary
	K-trivials are never continuously random with N. Greenberg, A. Montalban and T. Slaman Submitted. Format: Summary
	Upper bounds on ideals in the Turing degrees with Andre Nies Submitted. Format: Summary
	Randomness Notions and Partial Relativization with Joe Miller and Andre Nies Submitted. Format: Summary
	Tracing and domination in the Turing degrees Submitted. Format: Summary

PhD Thesis:

Computability and Applications to Analysis University of Leeds, July 2004 Format: