Papers and preprints available online


Below is a list of my papers and preprints which are available online. Clicking on one of these links will take you to a pdf version of the paper.


The uniform content of partial and linear orders, with Eric Astor, Damir Dzhafarov and Jacob Suggs, submitted.

Effectiveness of Hindman's theorem for bounded sums, with Damir Dzhafarov, Carl Jockusch and Brown Westrick, submitted.

Computable reductions and reverse math, to appear in Proceedings Volume for CiE 2016.

Ramsey's theorem for singletons and strong computable reductions, with Damir Dzhafarov, Ludovic Patey and Brown Westrick, to appear in Proceedings of the AMS.

On the effectiveness of symmetry breaking, with Russell Miller and Rebecca Steiner, in "Language, Life, Limits: 10th Conference of Computability in Europe, CiE 2014", 2014, 314-323.

Degrees that are low for isomorphism, with Johanna Franklin, Computability 3 (2), 2014, 73-89.

Separating principles below Ramsey's Theorem for Pairs, with Manny Lerman and Henry Towsner, Journal of Math Logic, 13(2), 2013.

Local computability for ordinals, with Johanna Franklin, Asher Kach and Russell Miller, in "The Nature of Computation: 9th Conference of Computability in Europe, CiE 2013", Lecture Notes in Computer Science 7921, 2013, 161-170.

Degrees of orders on torsion-free abelian groups, with Asher Kach and Karen Lange, Annals of Pure and Applied Logic 164 (7-8), 2013, 822-836.

Jump degrees of torsion free abelian groups, with Brooke Andersen, Asher Kach and Alexander Melnikov, Journal of Symbolic Logic 77 (4), 2012, 1067-1100.

Reverse mathematics and infinite traceable graphs, with Peter Cholak and David Galvin, Math Logic Quarterly 58 (1-2), 2012, 18-28.

Lowness notions, measure and domination with Bjoern Kjos-Hanssen and Joe Miller, Journal of the London Mathematical Society 85 (3), 2012, 869-888.

Cappable CEA sets and Ramsey's Theorem with Asher Kach and Manny Lerman, in "Proceedings of the 11th Asian Logic Conference", edited by Arai, Feng, Kim, Wu and Yang, World Scientific, 2012, 114-127.

Ordering free products in reverse mathematics, in "Foundational Adventures: Essays in Honors of Harvey M. Friedman", edited by Neil Tennant, Templeton Press (online) and College Publications London, 2011.

The complexity of central series in nilpotent computable groups with Barbara Csima, Annals of Pure and Applied Logic 162 (8), 2011, 667-678.

Embeddings of computable structures with Asher Kach and Oscar Levin, Notre Dame Journal of Formal Logic 51 (1), 2010, 55-68.

Stability and posets with Carl Jockusch Jr., Bart Kastermans, Steffen Lempp and Manny Lerman, Journal of Symbolic Logic 74 (2), June 2009, 693-711.

Self-embeddings of computable trees with Stephen Binns, Bjorn Kjos-Hanssen, Manny Lerman and Jim Schmerl, Notre Dame Journal of Formal Logic 49 (1), 2008, 1-38.

On the computability theoretic complexity of trivial, strongly minimal models with Bakhadyr Khoussainov, Chris Laskowski and Steffen Lempp, Proceedings of the AMS 135 (11), November 2007, 3711-3721.

Thin classes of separating sets, in Advances in Logic: The North Texas Logic Conference, Contemporary Mathematics 425, edited by Gao, Jackson and Zhang, 2007, 67-86.

Embedding finite lattices into the computably enumerable degrees - a status survey with Steffen Lempp and Manuel Lerman, in Logic Colloquium '02, edited by Chatzidakis, Koepke and Pohlers, AK Peters, 2006, 206-229.

On a conjecture of Dobrinen and Simpson concerning almost everywhere domination with Stehpen Binns, Bjorn Kjos-Hanssen and Manny Lerman, Journal of Symbolic Logic 71 (1), March 2006, 119-136 .

A computably stable structure with no Scott family of finitary formulas with Peter Cholak and Richard Shore, Archive for Mathematical Logic 45, 2006, 519-538.

Enumerations in computable structure theory with Sergey Goncharov, Valentina Harizanov, Julia Knight, Charlie McCoy and Russell Miller, Annals of Pure and Applied Logic 136 (3), 2005, 219-246.

Computable categoricity for trees of finite height with Steffen Lempp, Charlie McCoy and Russell Miller, Journal of Symbolic Logic 70 (1), March 2005, 151-215.

Reverse mathematics, archimedean classes, and Hahn's Theorem with Rod Downey, "Reverse Mathematics 2001", edited by Stephen Simpson, AK Peters, 2005, 147-163.

Reverse mathematics and the equivalence of definitions for well and better quasi-orders with Peter Cholak and Alberto Marcone, Journal of Symbolic Logic 69 (3), September 2004, 683-712.

Effectiveness for infinite variable words and the Dual Ramsey Theorem with Joe Miller, Archive for Mathematical Logic 43 (4) May 2004, 543-555.

Computability-theoretic and proof-theoretic aspects of partial and linear orderings with Rod Downey, Denis Hirschfeldt and Steffen Lempp, Israel Journal of Mathematics 138, 2003, 271-289.

The Lindenbaum algebra of the theory of the class of all finite models (gzip ps file) with Steffen Lempp and Mikhail Peretyat'kin, Journal of Mathematical Logic 2 (2), November 2002, 145-225.

Pi^0_1 classes and orderable groups Annals of Pure and Applied Logic 115 (1-3), 2002, 279-302.

The computable dimension of ordered abelian groups with Sergey Goncharov and Steffen Lempp, Advances in Mathematics 175, 2002, 102-143.

Group theoretic properties of the group of all computable automorphisms of a countable dense linear order with Steffen Lempp, Charles McCoy, and Andrei Morozov, Order 19, 2002, 343-364.

Reverse mathematics and the Nielsen-Schreier Theorem with Rod Downey, Denis Hirschfeldt and Steffen Lempp, in "Proceedings of the International Conference in Logic Honoring Ershov on his 60th Birthday and Maltsev on his 90th Birthday", edited by Goncharov, Novisibirsk 2002, 59-71.

Friedberg numberings of families of n-computably enumerable sets with Sergey Goncharov and Steffen Lempp, Algebra and Logic 41 (2), March 2002, 81-86.

A Delta^0_2 set with no infinite low set is either it or its complement with Rod Downey, Denis Hirschfeldt and Steffen Lempp, Journal of Symbolic Logic 66 (3), September 2001, 1371-1381.

On the filter of computable enumerable supersets of an r-maximal set with Steffen Lempp and Andre Nies, Archive for Mathematical Logic 40 (6), August 2001, 415-423.

Pi^1_1-CA_0 and order types of countable ordered groups Journal of Symbolic Logic 66 (1), March 2001, 192-206.

Ordered groups: a case study in reverse mathematics Bulletin of Symbolic Logic 5 (1), March 1999, 45-58.

Reverse mathematics and ordered groups Notre Dame Journal of Formal Logic 39 (2), Spring 1998, 157-189.