Carl G. Jockusch's Home Page

Professor Emeritus
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, Illinois 61801-2975
e-mail: jockusch@math.uiuc.edu

General Information

B.A. (with Highest Honors) Swarthmore College, 1963.
Ph.D. MIT, thesis advisor Hartley Rogers, 1966.
Retired in 2004.
Elected a Fellow of the American Mathematical Society in 2014.

Area of Specialization

Mathematical logic, especially computability theory (recursion theory) and its connections with other areas, such as model theory, combinatorics, and asymptotic density. For information on the program in mathematical logic at UIUC, click here.

Publications

List of Publications

Online Articles:

C. Jockusch and T. Lakins, Generalized r-cohesiveness and the arithmetical hierarchy: a correction to ``Generalized cohesiveness'' Journal of Symbolic Logic 67 (2002), 1078-1082. (ps or pdf)
C. Jockusch, A. Li, and Y. Yang, A join theorem for the computably enumerable degrees, Transactions of the American Mathematical Society , 356 (2004), 2557-2568. (ps or pdf)
P. Cholak, M. Giusto, J. Hirst, and C. Jockusch, Free sets and reverse mathematics, to pp. 104-119 in Reverse Mathematics 2001 , edited by S. Simpson, in the series Lecture Notes in Logic, Association for Symbolic Logic, 2005. (ps or pdf)
R. Coles, R. Downey, C. Jockusch and G. LaForte, Completing pseudojump operators, Annals of Pure and Applied Logic , 136 (2005), 297-333. (ps or pdf)
R. Downey, C. Jockusch and J. Miller, On self-embeddings of computable linear orderings , Annals of Pure and Applied Logic , 136 (2005), 297-333. pdf
D. Hirschfeldt, B. Kjos-Hanssen, C. Jockusch, S. Lempp, and T. Slaman, The strength of some combinatorial principles related to Ramsey's theorem for pairs, pp. 143 - 161 in Computational Prospects of Infinity , edited by Chitat Chong, Qi Feng, Theodore A. Slaman, W. Hugh Woodin, and Yue Yang, Vol. 15 in the Lecture Note Series of the Institute for Mathematical Sciences, National University of Singapore, published by World Scientific, New Jersey, London, Singapore, Beijing, Shanghai, Hong Kong, Taipei, Chennai, 2008. pdf
Angsheng Li and Carl Jockusch, Restricted jump interpolation in the dce degrees, Mathematical Structures in Computer Science , Vol. 16, issue 05, Oct. 2006, pp 841--865. pdf
John Chisholm, Jennifer Chubb, Valentina Harizanov, Carl Jockusch, Timothy McNicholl, and Sarah Pingrey, Strong degree spectra of relations and $\Pi^0_1$ classes, J. Symbolic Logic 72 (2007), 1003-1018. pdf
Valentina Harizanov, Carl Jockusch, and Julia Knight, Chains and antichains in partial orderings, Archive for Mathematical Logic 48 (2009), 39-53. pdf
Damir Dzhafarov and Carl Jockusch, Ramsey's theorem and cone avoidance, J. Symbolic Logic 74 (2) (2009), 557-578. pdf
Carl Jockusch, Bart Kastermans, Steffen Lempp, Manuel Lerman, and Reed Solomon, Stability and posets, J. Symbolic Logic 74 (2) (2009), 693-711. pdf
Peter A. Cholak, Carl G. Jockusch, Jr., and Theodore A. Slaman, Corrigendum to "On the strength of Ramsey's Theorem for pairs", J. Symbolic Logic , 74 (4) (2009), 1438-1439. pdf
R. Downey, N. Greenberg, C. Jockusch, and K. Milans, Binary subtrees with few labeled paths, Combinatorica 31 (3) (2011), 285-303. pdf
Carl G. Jockusch, Jr. and Paul Schupp, Generic computability, Turing degrees, and asymptotic density, Journal of the London Mathematical Society 85 (2) (2012), 472-490. pdf
Carl G. Jockusch, Jr. and Andrew E. M. Lewis, Diagonally non-computable functions and bi-immunity, J. Symbolic Logic, 78 (3) (2013), 977-988. pdf
Rodney G. Downey, Carl G. Jockusch, Jr. and Paul Schupp, Asymptotic density and computably enumerable sets, J. Mathematical Logic , 13 (2) (2013), 1350005 (43 pages). pdf
Rod Downey, Carl Jockusch, Timothy H. McNicholl, and Paul Schupp, Asymptotic density and the Ershov hierarchy, Mathematical Logic Quarterly 61 (2015), 189--195. pdf
Uri Andrews, Mingzhong Cai, David Diamondstone, Carl Jockusch, and Steffen Lempp, Asymptotic density, computable traceability and 1-randomness, Fundamenta Mathematicae 234 (2016), 41--53. pdf
Denis Hirschfeldt, Carl Jockusch, Timothy H. McNicholl, and Paul Schupp, Asymptotic density and the coarse computability bound, Computability 5 (2016), 13--27. pdf
Denis Hirschfeldt, Carl Jockusch, Rutger Kuyper, and Paul Schupp, Coarse reducibility and algorithmic randomness, to appear in J. Symbolic Logic . pdf
Denis Hirschfeldt and Carl Jockusch, On notions of computability theoretic reduction between $\Pi^1_2$ principles, preprint of an article published in J. Mathematical Logic 6, Issue 01 (2016), 1650002 (59 pages). pdf
Carl Jockusch, Herrmann's beautiful theorem on computable partial orderings, in Computability and Complexity , edited by Adam Day, Michael Fellows, Noam Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer, 2017. pdf
Damir Dzhafarov, Carl Jockusch, Reed Solomon, and Linda Brown Westrick, Effectiveness of Hindman's theorem for bounded sums, in Computability and Complexity , edited by Adam Day, Michael Fellows, Noam Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer, 2017. pdf
Carl Jockusch and Paul Schupp, Asymptotic density and the theory of computability : A partial survey, in Computability and Complexity , edited by Adam Day, Michael Fellows, Noam Greenberg, Bakhadyr Khoussainov, Alexander Melnikov, and Frances Rosamond, Lecture Notes in Computer Science, Springer, 2017. pdf
Barbara Csima, Damir Dzhafarov, Denis Hirschfeldt, Carl Jockusch, Reed Solomon, and Linda Brown Westrick, The reverse mathematics of Hindman's Theorem for sums of exactly two elements, Computability 8 (2019), 253 - 263. pdf
Eric Astor, Denis Hirschfeldt and Carl Jockusch, Dense computability, upper cones, and minimal pairs, Computability 8 (2019), 155 - 177. pdf
Denis Hirschfeldt, Carl Jockusch, and Paul Schupp, Coarse computability, the density metric, Hausdorff distances between Turing degrees, perfect trees, and reverse mathematics (with Denis Hirschfeldt and Paul Schupp), submitted for publication. pdf

PhD Students

Paul F. Cohen
David Posner
Linda Jean Richter (deceased)
Jeanleah Mohrherr
Stuart Kurtz
Michael Ingrassia
Larry Welch
Richard Blaylock
Tamara Hummel (now named Tamara Lakins)
Benjamin Schaeffer
Kejia Ho
Linda Lawton
Joseph Mileti