Research Interests
Interactions of mathematical logic (computability theory, set theory, model theory) with algebra and combinatorics.
Interactions of mathematical logic (computability theory, set theory, model theory) with algebra and combinatorics.
The complexity of primes in computable UFDs (with D. Dzhafarov), pdf, Notre Dame Journal of Formal Logic, 59 (2018), no. 2, 139-156.
Irreducibles and primes in computable integral domains (with L. Evron and E. Ratliff-Crain), pdf, in Computability and Complexity (2017), edited by Adam Day, Michael Fellows, Noam Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer.
On uniform relationships between combinatorial problems (with F. Dorais, D. Dzhafarov, J. Hirst, and P. Shafer), pdf, Transactions of the American Mathematical Society, 368 (2016), no. 2, 1321-1359.
Reverse mathematics and Ramsey's property for trees (with J. Corduan and M. Groszek), Journal of Symbolic Logic, 75 (2010), no. 3, 945-954.
The strength of the rainbow Ramsey theorem (with B. Csima), pdf, Journal of Symbolic Logic, 74 (2009), no. 4, 1310-1324.
The canonical Ramsey theorem and computability theory, pdf, Transactions of the American Mathematical Society, 360 (2008), 1309-1340.
Ideals in computable rings (with R. Downey and S. Lempp), pdf, Journal of Algebra, 314 (2007), no. 2, 872-887.
Subspaces of computable vector spaces (with R. Downey, D. Hirschfeldt, A. Kach, S. Lempp, and A. Montalbán), pdf, Journal of Algebra, 314 (2007), no. 2, 888-894.
Partition theorems and computability theory, pdf ps, dissertation at UIUC. Thesis Advisor: Carl Jockusch.
Partition theorems and computability theory, Bulletin of Symbolic Logic, vol. 11 #3 (2005), 411--427.