I study the computational complexity of various algebraic structures, including various kinds of graphs, groups, and homogeneous models, highly regular structures important in model theory. Some of my work from the computational perspective has led me to questions that are more algebraic or model-theoretic in nature. Separately, I am interested in aspects of the structure of the computably enumerable sets under inclusion, an object of intense study in classical computability theory.

Truncation-closed subfields of a Hahn Field, J. Knight and K. Lange, submitted. (pdf)

D-maximal sets, P. Cholak, P. Gerdes, and K. Lange, Journal of Symbolic Logic, 80(4) (2015), 1182-1210. (pdf)

On n-tardy sets, P. Cholak, P. Gerdes, and K. Lange, Annals of Pure and Applied Logic, 163(9) (2012), 1252-1270. (pdf)

Induction, bounding, weak combinatorial principles, and the homogeneous model theorem, D. Hirschfeldt, K. Lange, and R. Shore, accepted by Memoirs of the American Mathematical Society (2015). (pdf)

The arithmetical hierarchy in the setting of ω

Complexity of structures associated with real closed fields, J. Knight and K. Lange, Proceedings of the London Mathematical Society, Third Series, 107(1) (2013), 177-197. (pdf)

Degrees of orders on torsion-free abelian groups, A. Kach, K. Lange, and D. Solomon, Annals of Pure and Applied Logic, 164(7-8) (2013), 822-836. (pdf)

Real closed exponential fields, P. D'Aquino, J. Knight, S. Kuhlmann, and K. Lange, Fundamenta Mathematicae, 219(2) (2012), 163-190. (pdf)

Describing free groups, J. Carson, V. Harizanov, J. Knight, K. Lange, C. Maher, C. McCoy, A. Morozov, S. Quinn, and J. Wallbaum, Transactions of the American Mathematical Society, 364(11) (2012), 5715-5728. (pdf)

Limit computable integer parts, P. D'Aquino, J. Knight, and K. Lange, Archive for Mathematical Logic, 50(7-8) (2011), 681-695. (pdf)

Erratum Archive for Mathematical Logic, 54(3-4) (2015), 487-489.

A characterization of the 0-basis homogeneous bounding degrees, K. Lange, Journal of Symbolic Logic 75 No. 3 (2010), 971-995. (pdf)

The degree spectra of homogeneous models, K. Lange, Journal of Symbolic Logic, vol. 73 No. 3 (2008), 1009-1028. (pdf)

Computability of homogeneous models, K. Lange and R. Soare, Notre Dame Journal of Formal Logic, vol. 48 (2007), 143-170. (pdf)

The computational complexity of homogeneous models, K. Lange, Ph.D. thesis, Advisors: Robert Soare and Denis Hirschfeldt, University of Chicago (2008). (pdf)

A valuation theoretic characterization of recursively saturated real closed fields, P. D'Aquino, S. Kuhlmann, and K. Lange, Journal of Symbolic Logic, 80(1) (2015), 194-206. (pdf)

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