Preprints and Publications

1. 1.The Arithmetic Theory of the Hilbert Basis Theorem for Modules.
   Submitted.
   
   

2. 2.On the Computability of the Krull Intersection Theorem.
   Submitted.
   
   

3. 3.On the existence of infinite monomial division chains with finitely many indeterminates.
   To appear in The Proceedings of Computability in Europe, 2024.
   
   

4. 4.Formal Power Series in Second-Order Arithmetic.
   To appear in the Proceedings of the 14th Panhellenic Logic Symposium.
   
   

5. 5.Computability and Combinatorial Aspects of Minimal Prime Ideals in Noetherian Rings.
   Submitted.
   
   

6. 6.The complexity of module radicals.
   Notre Dame Journal of Formal Logic, vol. 62(2) 353--368 (2021).
   
   

7. 7.Transfinitely valued Euclidean domains have arbitrary indecomposable order type.
   (with P.P. Nielsen and V. Tombs)
   Communications in Algebra, vol. 47(3) 1105--1113 (2019).
   
   

8. 8.The computability, definability, and proof theory of Artinian rings.
   Advances in Mathematics, vol. 341(1) 1--39 (2019)
   
   

9. 9.The complexity of ascendant sequences in locally nilpotent groups.
   (with R. A. Shore)
   International Journal of Algebra and Computation, vol. 24(2) 189--205 (2014)
   
   

10. 10.Infinite dimensional proper subspaces of computable vector spaces.
    Journal of Algebra, vol. 406(1) 346--375 (2014)
    
    

11. 11.Random reals, the rainbow Ramsey theorem, and arithmetic conservation.
    (with T. A. Slaman)
    Journal of Symbolic Logic, vol. 78(1) 195--206 (2013)
    
    

12. 12.Galvin’s “Racing Pawn” game, internal hyperarithmetic comprehension, and the law of excluded middle.
    (with N. Greenberg and D. Turetsky)
    Notre Dame Journal of Formal Logic, vol. 54(2) 233--252 (2013)
    
    

13. 13.Comparing theorems of hyperarithmetic analysis with the arithmetic Bolzano-Weierstrass theorem.
    Transactions of the AMS, vol. 364(9) 4465--4494 (2012)
    
    

14. 14. A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one.
    Journal of Symbolic Logic, vol. 77(2) 447--474 (2012)
    
    

15. 15. Effectively approximating measurable sets by open sets.
    Theoretical Computer Science, vol. 428(1) 36--46 (2012)
    
    

16. 16. A measure-theoretic proof of Turing incomparability.
    Annals of Pure and Applied Logic, vol. 162(1) 83--88 (2010)
    
    

17. 17. Chain conditions in computable rings.
    Transactions of the AMS, vol. 362(12) 6523--6550 (2010)
    
    

18. 18. On the complexity of radicals in noncommutative rings.
    Journal of Algebra, vol. 322(10) 3670--3680 (2009)
    
    

19. 19. Effective packing dimension of Π1-classes.
    Proceedings of the AMS, vol. 136(10) 3655--3662 (2008)
    
    

20. 20. Classifying model-theoretic properties.
    Journal of Symbolic Logic, vol. 73(3) 885--905 (2008)
    
    

21. 21. Tensor operators and constructing indecomposable representations of semidirect product groups. (with J. Repka)
    Journal of Mathematical Physics, vol. 44(6) 2679--2691 (2003)
    

Applications of computability theory. PhD thesis, University of Chicago (2009)