Denis Hirschfeldt's CV

Denis Roman Hirschfeldt

Department of Mathematics
University of Chicago
5734 S. University Ave.
Chicago, IL 60637
U.S.A.
1-773-702-7375
1-773-702-9787 (fax)
drh@math.uchicago.edu
www.math.uchicago.edu/~drh

Citizenship

Brazilian (permanent resident of the U.S.A.)

Research Interests

Computability Theory, Computable Mathematics, Reverse Mathematics, Algorithmic Randomness

Education

Ph.D. in Mathematics, Cornell University, August 1999 (advisor: Richard A. Shore)
M.S. in Computer Science, Cornell University, August 1998
B.A. in Mathematics, University of Pennsylvania, May 1993

Employment

Professor, University of Chicago, from October 2008
Associate Professor, University of Chicago, October 2005 - September 2008
Assistant Professor, University of Chicago, September 2002 - September 2005
Dickson Instructor of Mathematics, University of Chicago, December 2000 - September 2002
Postdoctoral Fellow, Victoria University of Wellington, August 1999 - December 2000

Grants

National Science Foundation Focused Research Group Grant (Lead PI, with several other researchers), 2019 -
National Science Foundation Research Grants, 2002 - 2015 and 2016 -
University of Chicago Center in Paris Faculty Grant, awarded in 2020
Simons Foundation Collaboration Grant for Mathematicians, 2015 - 2016
National Science Foundation Focused Research Group Grant (with several other researchers), 2007 - 2011
Air Force Office of Scientific Research Grant, 2009
Templeton Foundation "Exploring the Infinite" Program Grant (with other researchers), 2008 - 2009
National Science Foundation U.S.-Russia Binational Grant (with several other researchers), 2006 - 2009
Research Incentive Grant from the University of Chicago Department of Computer Science, 2002
Research Incentive Grant from the University of Chicago Department of Mathematics, 2002 - 2005
Associate investigator on a research grant from the Marsden Fund for Basic Science of New Zealand, 2004 - 2006, awarded to the Department of Computer Science, University of Auckland, New Zealand

Honors and Awards

2016 Shoenfield Prize of the Association for Symbolic Logic
2010 Shoenfield Prize of the Association for Symbolic Logic
Visiting Scholar at the University of Notre Dame, April 2005
Visiting Assistant Professorship at the University of Wisconsin--Madison, September 2003
1999 Sacks Prize of the Association for Symbolic Logic
Honorary Fellowship at the University of Wisconsin-Madison, August - September 1999
Alfred P. Sloan Doctoral Dissertation Fellowship, Spring 1998 - Fall 1999
Research Fellowship at Victoria University of Wellington, supported by the Marsden Fund for Basic Science of New Zealand, October - November 1998
Robert John Battig Prize of the Cornell Department of Mathematics, 1998

Talks

Fourth Workshop on Digitalization and Computble Models, October 2022 (online meeting)
Online Conference in Honor of Anil Nerode's 90th Birthday, June 2022
Special Session on Reverse Mathematics and Combinatorial Principles, Logic Colloquium, June-July 2022, Reykjavik, Iceland (remote talk)
Algorithmic Presentations in Mathematics, November, 2021, Sochi, Russia (hybrid meeting)
Logical Perspectives, June 2021, Moscow, Russia (hybrid meeting)
Computability Theory Meeting, April-May, 2021, Oberwolfach, Germany (hybrid meeting)
Plenary Lecture, South Eastern Logic Symposium, February 2020, Gainesville, FL
Special Session on Computability Theory, CMS Winter Meeting, December 2019, Toronto, Canada
A Conversation on Professional Norms in Mathematics, September 2019, Baltimore, MD
Steffen Lempp's 60th Birthday Conference, September 2019, Madison, WI
Special Session on Computability, Logic Colloquium, August 2019, Prague, Czech Republic
Short Course on the Priority Method, CUSO Summer School on Recursion Theory and Philosophy, August 2019, Geneva, Switzerland
Columbia College Science and Mathematics Colloquium Series, April 2019, Chicago, IL
Special Session on Computability Theory, AMS Sectional Meeting, April 2019, Hartford, CT
Special Session on Computability, Complexity, and Learning, AMS Sectional Meeting, March 2019, Honolulu, HI
Workshop on Computability Theory and Applications, June 2018, Waterloo, Canada
Special Session on Computability Theory, Association for Symbolic Logic Annual Meeting, May 2018, Macomb, IL
Ng Kong Beng Public Lecture, September 2017, Singapore
Aspects of Computation, September 2017, Singapore
Plenary Lecture, Logic Colloquium, August 2017, Stockholm, Sweden
Tutorial on Computability Theory, Reverse Mathematics, and Combinatorial Principles, Computability in Europe, June 2017, Turku, Finland
Logic at UC Berkeley, May 2017, Berkeley, CA
Tutorial on Reverse Mathematics, NZMRI Summer School, January 2017, Napier, New Zealand
Keynote Talk, Computability and Complexity Symposium, January 2017, Raumati, New Zealand
Tutorial on the Computability Theory and Reverse Mathematics of Combinatorial Principles, Association for Symbolic Logic Annual North American Meeting, May 2016, Storrs, CT
Measuring the Complexity of Computational Content: Weihrauch Reducibility and Reverse Analysis, September 2015, Schloss Dagstuhl Research Center for Computer Science, Germany
Computability, Analysis, and Geometry, March 2015, Banff International Research Station, Canada
Plenary Lecture, Southeastern Logic Symposium, February - March 2015, Gainesville, FL
Special Session on Computability Theory, CMS Winter Meeting, December 2014, Hamilton, Canada
Special Session on Computability Across Mathematics, AMS Sectional Meeting, October 2013, St. Louis, MO
Buenos Aires Semester in Computability, Complexity and Randomness, May 2013, Buenos Aires, Argentina
Special Session on Computable Structure/Model Theory, Association for Symbolic Logic Annual Meeting, May 2013, Waterloo, Canada
Special Session on Computability and Complexity in Discrete and Continuous Worlds, AMS Sectional Meeting, April 2013, Ames, IA
Midwest Computability Seminar, April 2013, Chicago, IL
Special Session on Effective Algebra and Model Theory, AMS Annual Meeting, January 2013, San Diego, CA
Invited Lecture, Logic and Computability Session, 4th Latin American Congress of Mathematicians, August 2012, Córdoba, Argentina
The Incomputable, June 2012, Chicheley Hall, UK
Plenary Lecture, 15th Latin American Symposium on Mathematical Logic, June 2012, Bogotá, Colombia
Short Course on Reverse Mathematics of Combinatorial Principles, April-May 2012, Hebrew University, Israel
Special Session on Computability and its Applications, AMS Sectional Meeting, November 2010, South Bend, IN
Short Course on Reverse Mathematics of Combinatorial Principles, Asian Initiative for Infinity Summer School, July 2010, Singapore
Plenary Lecture, Computability in Europe, June - July 2010, Ponta Delgada, Portugal
5th Conference on Logic, Computability, and Randomness, May 2010, South Bend, IN
Southeastern Logic Symposium, February 2010, Gainesville, FL
Special Session on Computability Theory, Logic Colloquium, August 2009, Sofia, Bulgaria
Foundational Adventures: A Conference in Honor of Harvey M. Friedman, May 2009, Columbus, OH
Marden Lecture, University of Wisconsin-Milwaukee, April 2009, Milwaukee, WI
Tutorial on Algorithmic Randomness, NZIMA / NZMRI summer workshop, January 2009, Napier, New Zealand
Computability, Reverse Mathematics, and Combinatorics, December 2008, Banff International Research Station, Canada
Special Session on Computability Theory and Effective Algebra, AMS Sectional Meeting, October 2008, Middletown, CT
Workshop on the Effective Mathematics of the Uncountable, August 2008, New York, NY
Memorial Meeting in Honor of Andrei Muchnik, March 2008, Moscow, Russia
Special Session on Computability Theory, Joint AMS-NZMS Meeting, December 2007, Wellington, New Zealand
Keynote Talk, Algorithmic-Logical Theory of Infinite Structures, October - November 2007, Schloss Dagstuhl Research Center for Computer Science, Germany
Keynote Address, 8th Graduate Student Conference in Logic, April 2007, Chicago, IL
Plenary Lecture, Association for Symbolic Logic Annual Meeting, March 2007, Gainesville, FL
Workshop on Model Theory and Computable Model Theory, February 2007, Gainesville, FL
Tutorial on Algorithmic Randomness, Third International Conference on Computability and Complexity in Analysis, November 2006, Gainesville, FL
Special Session on Computability Theory in Honor of Manuel Lerman's Retirement, AMS Sectional Meeting, October 2006, Storrs, CT
Special Session on Randomness and Real Computation, Theory and Applications of Models of Computation (TAMC 06), May 2006, Beijing, China
Special Session on Model Theory and Computability, AMS Sectional Meeting, April 2006, South Bend, IN
Kolmogorov Complexity and Applications, January - February 2006, Schloss Dagstuhl Research Center for Computer Science, Germany
Computational Prospects of Infinity, June - August 2005, Singapore
11th Southeastern Logic Symposium, April 2005, Gainesville, FL
Special Session on Computability and Randomness, Association for Symbolic Logic Annual Meeting, March 2005, Stanford, CA
UCLA Logic Meeting, February 2005, Los Angeles, CA
Special Session on Reverse Mathematics, AMS Annual Meeting, January 2005, Atlanta, GA
North Texas Logic Conference, October 2004, Denton, TX
10th Southeastern Logic Symposium, March 2004, Gainesville, FL
Logic Section, 12th International Congress of Logic Methodology and Philosophy of Science, August 2003, Oviedo, Spain
Plenary Lecture, Greater Boston Logic Meeting, May 2003, Boston, MA
Kolmogorov Complexity and Applications, April 2003, Schloss Dagstuhl Research Center for Computer Science, Germany
Special Session on Computability and Models, AMS Annual Meeting, January 2003, Baltimore, MD
Special Session on Effectiveness Questions in Model Theory, AMS Sectional Meeting, October 2002, Madison, WI
Midwest Model Theory Meeting, April 2002, Chicago, IL
Special Session on Computability Theory with Applications, AMS Annual Meeting, January 2002, San Diego, CA
Computability and Complexity in Analysis, November 2001, Schloss Dagstuhl Research Center for Computer Science, Germany
26th International Symposium on Mathematical Foundations of Computer Science (MFCS 2001), August 2001, Mariánské Lázne, Czech Republic
Special Session on Computability Theory, Association for Symbolic Logic European Summer Meeting, August 2001, Vienna, Austria
Plenary Lecture, Association for Symbolic Logic Annual Meeting, March 2001, Philadelphia, PA
18th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2001), February 2001, Dresden, Germany
Computability Theory Meeting, January 2001, Oberwolfach, Germany
Plenary Lecture, Association for Symbolic Logic Winter Meeting, January 2001, New Orleans, LA
Plenary Lecture, Logic and Applications Meeting, May 2000, Novosibirsk, Russia
Special Session on Computability Theory, AMS Sectional Meeting, March 1999, Gainesville, FL
Special Session on Computability Theory, Association for Symbolic Logic European Summer Meeting, August 1998, Prague, Czech Republic
Special Session on Computability Theory, AMS Sectional Meeting, October 1997, Milwaukee, WI
Colloquia and seminars at various universities

Courses Taught

Undergraduate Courses: Mathematical Logic I and II, Effective Randomness and Dimension, Point-Set Topology, Introduction to Algebraic Topology, Abstract Linear Algebra, Algebra III, Basic Geometry, Galois Theory, First Semester Calculus
Graduate Courses: Computability Theory I and II, Set Theory I and II, Computable Model Theory I and II, Intuitionistic Logic and Constructive Mathematics, Model Theory III, Effective Randomness I and II, Effective Dimension, Descriptive Set Theory I and II, Advanced Topics in Logic

Graduate Students Examined or Advised

Secondary advisor for Barbara Csima's Ph.D. Dissertation in Mathematics, University of Chicago, 2003
Advisor^* for Kenneth Harris's Ph.D. Dissertation in Mathematics and Computer Science, University of Chicago, 2007
Advisor^* for Karen Lange's Ph.D. Dissertation in Mathematics, University of Chicago, 2008
Advisor^* for Chris Conidis' Ph.D. Dissertation in Mathematics, University of Chicago, 2009
Advisor^* for Rachel Epstein's Ph.D. Dissertation in Mathematics, University of Chicago, 2010
Advisor^* for Damir Dzhafarov's Ph.D. Dissertation in Mathematics, University of Chicago, 2011
Advisor^* for David Diamondstone's Ph.D. Dissertation in Mathematics, University of Chicago, 2011
Advisor^* for Matthew Wright's Ph.D. Dissertation in Mathematics, University of Chicago, 2013
Advisor^* for Jonny Stephenson's Ph.D. Dissertation in Mathematics, University of Chicago, 2014
Advisor^* for Eric Astor's Ph.D. Dissertation in Mathematics, University of Chicago, 2015
Advisor for Sarah Reitzes' Ph.D. Dissertation in Mathematics, University of Chicago, 2022
Advisor^** for Isabella Scott's Ph.D. Dissertation in Mathematics, University of Chicago, 2024
Advisor^** for Gabriela Laboska's Ph.D. Dissertation in Mathematics, University of Chicago, in progress
Advisor^*** for Tiago Royer's Ph.D. Dissertation in Computer Science, University of Chicago, in progress
Outside examiner for Justin Miller's Ph.D. Dissertation in Mathematics, University of Notre Dame, 2021
Outside examiner for Michael McInerney's Ph.D. Dissertation in Mathematics, Victoria University of Wellington, New Zealand, 2016
Outside examiner for Rutger Kuyper's Ph.D. Dissertation in Mathematics, Radboud University Nijmegen, The Netherlands, 2015
Outside examiner for Benoit Monin's Ph.D. Dissertation in Computer Science, Paris 7 University, France, 2014
Outside examiner for Adam Day's Ph.D. Dissertation in Mathematics, Victoria University of Wellington, New Zealand, 2011
Outside examiner for Sasha Rubin's Ph.D. Dissertation in Computer Science, University of Auckland, New Zealand, 2004
Outside examiner for Joseph Mileti's Ph.D. Dissertation in Mathematics, University of Illinois at Urbana-Champaign, 2004

Advisor^** for Gabriela Pinto's Ph.D. Dissertation in Mathematics, University of Chicago, in progress

* Jointly advised with Robert Soare
** Jointly advised with Maryanthe Malliaris
*** Jointly advised with Janos Simon

Professional Activities and Memberships

Editor, De Gruyter Series in Logic and its Applications, 2016 -
Co-organizer of the Midwest Computability Seminar, 2012 -
Member of the steering committee for the Computability, Complexity, and Randomness conference series, 2009 -
Graduate student ombudsperson, University of Chicago Department of Mathematics, 2016 -
President, University of Chicago AAUP Advocacy Chapter, 2017 -
Member of the Committee on Prizes and Awards of the Association for Symbolic Logic, 2021 - 2025
Editor, Lecture Notes in Logic Series, 2020 - 2022
Co-organizer of the Workshop on Effective Methods in Measure and Dimension at the American Institute of Mathematics, 2022
Co-organizer of the Special Session At the Intersection of Computability and Other Areas of Mathematics, Computability in Europe 2022, Swansea, UK, 2022
Co-organizer of the Workshop on Reverse Mathematics and its Philosophy, Paris, France 2022
Member of the organizing committee for the Conference on New Directions in Computability Theory, Luminy, France, 2022
Member of the Executive Committee of the Association for Symbolic Logic, 2019 - 2021
Panel discussion moderator, Association for Symbolic Logic Annual Meeting, South Bend, IN, 2021 (virtual meeting)
Reviewer for Benoit Monin's habilitation (HDR) dissertation, 2021
Co-organizer of the Workshop on Algorithmic Randomness at the American Institute of Mathematics, 2020 (virtual meeting)
Chair of the program committee for the Association for Symbolic Logic North American Annual Meeting, Irvine, CA, 2020 (canceled due to the public health emergency)
Member of the program committee for the Symposium on Logical Foundations of Computer Science (LFCS '20), Deerfield Beach, FL, 2020
Member of the Physical Sciences Collegiate Division Governing Committee, University of Chicago, 2010 - 2019
Co-organizer of the Workshop on Reverse Mathematics of Combinatorial Principles, Oaxaca, Mexico, 2019
Member of the Council of the Faculty Senate, University of Chicago, 2012 - 2014 and 2015 - 2018
Member of the program commitee for the Workshop on Ramsey Theory and Computability, Rome, Italy, 2018
Member of the program committee for the Fifteenth International Conference on Computability and Complexity in Analysis, Lake Kochel, Germany, 2018
Member of the program committee for the Symposium on Logical Foundations of Computer Science (LFCS '18), Deerfield Beach, FL, 2018
Second vice-president, University of Chicago AAUP Advocacy Chapter, 2015 - 2017
Co-organizer of the Special Session on Computable Structure Theory, Association for Symbolic Logic North American Annual Meeting, Boise, ID, 2017
Co-director of graduate studies, University of Chicago Department of Mathematics, 2014 - 2016
Co-chair of the program committee for Computability, Complexity, and Randomness, Honolulu, HI, 2016
Member of the program committee for the Symposium on Logical Foundations of Computer Science (LFCS '16), Deerfield Beach, FL, 2016
Member of the organizing committee for New Challenges in Reverse Mathematics, Institute for Mathematical Sciences, Singapore, 2016
Co-organizer of the Special Session on Computability Theory and Applications, American Mathematical Society Sectional Meeting, Chicago, IL, 2015
Co-organizer of the Chicago Logic Day, Chicago, IL, 2013
Editor for the Journal of Symbolic Logic, 2010 - 2012
Member of the Association for Symbolic Logic Committee on Meetings in North America, 2006 - 2011
Co-organizer of the Reverse Mathematics Workshop, Chicago, IL, 2011
Member of the program and organizing committees for Computability Theory and Applications: A Meeting in Honor of Robert I. Soare, Chicago, IL, 2011
Member of the program committee for Computability in Europe 2011, Sofia, Bulgaria, 2011
Co-organizer of the Workshop on Computability Theory, Paris, France, 2010
Member of the program committee for the 5th Conference on Logic, Computability, and Randomness, South Bend, IN, 2010
Member of the program committee for the 2nd Workshop on the Effective Mathematics of the Uncountable, New York, 2009
Co-organizer of the Workshop on Reverse Mathematics: Foundations and Applications, Chicago, IL, 2009
Member of the program committee for the 4th International Conference on Logic, Computability and Randomness, Luminy, France, 2009
Member of the program committee for the Symposium on Logical Foundations of Computer Science (LFCS '09), Deerfield Beach, FL, 2009
Member of the program committee for the Workshop on the Effective Mathematics of the Uncountable, New York, 2008
Member of the program committee for the Conference on Computability, Complexity, and Randomness, Nanjing, China, 2008
Co-organizer of the Workshop on Effective Randomness, Chicago, IL, 2007
Co-organizer of Topics in Computability: A Meeting in Honor of Richard A. Shore, Boston, 2007
Member of the program committee for the Conference on Logic, Computability, and Randomness, Buenos Aires, Argentina, 2007
Member of the program committee for the Symposium on Logical Foundations of Computer Science (LFCS'07), New York, 2007
Member of the program committee for the Third International Conference on Computability and Complexity in Analysis, Gainesville, FL, 2006
Co-organizer of the Workshop on Effective Randomness at the American Institute of Mathematics, 2006
Member of an Association for Symbolic Logic Nominating Committee, 2005
Reviews editor for the Bulletin of Symbolic Logic, 2004 - 2008
Member of the program committee for the Conference on Logic, Computability, and Randomness, Córdoba, Argentina, 2004
Member of the program committee for the Association for Symbolic Logic 2004 Annual Meeting, Pittsburgh, PA
Member of the program committee for the Association for Symbolic Logic 2003 Annual Meeting, Chicago, IL
Member of the organizing committee for the New Zealand Mathematics Research Institute Summer Meeting, Kaikoura 2000
Wrote the internal Journal of Symbolic Logic database and its web-based interface
Referee for various journals and reviewer for Mathematical Reviews
Member of various departmental and divisional committees
Member, American Mathematical Society, Association for Symbolic Logic, Mathematical Association of America, Computability in Europe, and American Association of University Professors

List of Publications

Books

Editor (with R. G. Downey): Aspects of Complexity: Minicourses in Algorithmics, Complexity, and Computational Algebra, NZMRI Summer Meeting, Kaikoura, New Zealand, January 7 - 15, 2000, de Gruyter Series in Logic and its Applications 4 (de Gruyter, 2001)
Algorithmic Randomness and Complexity (with R. G. Downey), Theory and Applications of Computability, Springer, New York, 2010
Editor (with N. Greenberg, R. Miller, and J. Hamkins): Effective Mathematics of the Uncountable, Lecture Notes in Logic, Association for Symbolic Logic / Cambridge University Press, 2013
Slicing the Truth: On the Computability Theoretic and Reverse Mathematical Analysis of Combinatorial Principles, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, World Scientific, 2014

Expository papers

Degree Spectra of Relations on Computable Structures, Bulletin of Symbolic Logic 6 (2000) 197 - 212
Calibrating Randomness (with R. Downey, A. Nies, and S. A. Terwijn), Bulletin of Symbolic Logic 12 (2006) 411 - 491
Five Papers on Reverse Mathematics and Ramsey-Theoretic Principles, Bulletin of Symbolic Logic 22 (2016) 526 - 530
Some Questions in Computable Mathematics, in Day, Fellows, Greenberg, Khoussainov, Melnikov, and Rosamond, eds., Computability and Complexity, Springer 2017, 22 - 55
Algorithmic Randomness (with R. Downey), Communications of the Association for Computing Machinery 62 (2019) 70 - 80
Computability and Randomness (with R. Downey), Notices of the American Mathematical Society 66 (2019) 1001 - 1012
Turning Coffee into Unions: Mathematicians and Collective Bargaining, in A Conversation on Professional Norms in Mathematics, Gerbelli-Gauthier, Harris, Hill, Karp, and Riehl (eds.), American Mathematical Society 2021, 112-137

Research papers

Undecidability and 1-types in Intervals of the Computably Enumerable Degrees (with K. Ambos-Spies and R. A. Shore), Annals of Pure and Applied Logic 106 (2000) 1 - 47
Degree Spectra of Intrinsically C.E. Relations, Journal of Symbolic Logic 66 (2001) 441 - 469
Prime Models of Theories of Computable Linear Orderings, Proceedings of the American Mathematical Society 129 (2001) 3079 - 3083
A Δ⁰₂ Set with no Infinite Low Subset in Either It or Its Complement (with R. G. Downey, S. Lempp, and R. Solomon), Journal of Symbolic Logic 66 (2001) 1371 - 1381
Degree Spectra and Computable Dimensions in Algebraic Structures (with B. Khoussainov, R. A. Shore, and A. M. Slinko), Annals of Pure and Applied Logic 115 (2002) 71 - 113
Degree Spectra of Relations on Structures of Finite Computable Dimension, Annals of Pure and Applied Logic 115 (2002) 233 - 277
Randomness, Computability, and Density (with R. G. Downey and A. Nies), SIAM Journal on Computing 31 (2002) 1169 - 1183 (extended abstract in A. Ferreira and H. Reichel (eds.), STACS 2001 Proceedings, Lecture Notes in Computer Science 2010 (Springer, 2001))
Degree Spectra of Relations on Computable Structures in the Presence of Δ⁰₂ Isomorphisms, Journal of Symbolic Logic 67 (2002) 697 - 720
Reverse Mathematics of the Nielsen-Schreier Theorem (with R. G. Downey, S. Lempp, and R. Solomon), in Proceedings of International Conferences on Mathematical Logic (Novosibirsk State University Press, 2002) 59 - 71
Realizing Levels of the Hyperarithmetic Hierarchy as Degree Spectra of Relations on Computable Structures (with W. M. White), Notre Dame Journal of Formal Logic 43 (2002) 51 - 64
Degree Spectra of Relations on Boolean Algebras (with R. G. Downey and S. S. Goncharov), Algebra and Logic 42 (2003) 105 - 111
Trivial Reals (with R. G. Downey, A. Nies, and F. Stephan), in R. Downey, D. Decheng, T. S. Ping, Q. Y. Hui, and M. Yasugi (eds.), Proceedings of the 7th and 8th Asian Logic Conferences (Singapore University Press and World Scientific, 2003) 103 - 131 (extended abstract in Electronic Notes in Theoretical Computer Science 66)
Computability-Theoretic and Proof-Theoretic Aspects of Partial and Linear Orderings (with R. G. Downey, S. Lempp, and R. Solomon), Israel Journal of Mathematics 138 (2003) 271 - 290
Uniformity in Computable Structure Theory (with R. G. Downey and B. Khoussainov), Algebra and Logic 42 (2003) 318 - 332
A Computably Categorical Structure Whose Expansion by a Constant Has Infinite Computable Dimension (with B. Khoussainov and R. A. Shore), Journal of Symbolic Logic 68 (2003) 1199 - 1241
Randomness and Reducibility (with R. G. Downey and G. LaForte), Journal of Computer and System Sciences 68 (2004) 96 - 114 (extended abstract in J. Sgall, A. Pultr, and P. Kolman (eds.), Mathematical Foundations of Computer Science 2001, Lecture Notes in Computer Science 2136 (Springer, 2001) 316 - 327)
Bounding Prime Models (with B. F. Csima, J. F. Knight, and R. I. Soare), Journal of Symbolic Logic 69 (2004) 1117 - 1142
Relativizing Chaitin's Halting Probability (with R. Downey, J. S. Miller, and A. Nies), Journal of Mathematical Logic 5 (2005) 167 - 192
Computable Trees, Prime Models, and Relative Decidability, Proceedings of the American Mathematical Society 134 (2006) 1495 - 1498
An Uncountably Categorical Theory whose Only Computably Presentable Model Is Saturated (with B. Khoussainov and P. Semukhin), Notre Dame Journal of Formal Logic 47 (2006) 63 - 71
Every 1-Generic Computes a Properly 1-Generic (with B. F. Csima, R. Downey, N. Greenberg, and J. S. Miller), Journal of Symbolic Logic 71 (2006) 1385 - 1393
Combinatorial Principles Weaker than Ramsey's Theorem for Pairs (with R. A. Shore), Journal of Symbolic Logic 72 (2007) 171 - 206
Bounding Homogeneous Models (with B. F. Csima, V. S. Harizanov, and R. I. Soare), Journal of Symbolic Logic 72 (2007) 305 - 323
Π⁰₁ Classes and Strong Degree Spectra of Relations (with J. Chisholm, J. Chubb, V. S. Harizanov, C. G. Jockusch, Jr., T. McNicholl, and S. Pingrey), Journal of Symbolic Logic 72 (2007) 1003 - 1018
Subspaces of Computable Vector Spaces (with R. Downey, A. M. Kach, S. Lempp, J. R. Mileti, and A. Montalbán), Journal of Algebra 314 (2007) 888 - 894
Using Random Sets as Oracles (with A. Nies and F. Stephan), Journal of the London Mathematical Society 75 (2007) 610 - 622
Order Computable Sets (with R. Miller and S. Podzorov), Notre Dame Journal of Formal Logic 48 (2007) 317 - 347
Undecidability of the Structure of the Solovay Degrees of C.E. Reals (with R. Downey and G. LaForte), Journal of Computer and System Sciences 73 (2007) 769 - 787
Limit Computability and Constructive Measure (with S. A. Terwijn), in Chong, Feng, Slaman, Woodin, and Yang (eds.), Computational Prospects of Infinity, Part II: Presented Talks, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 15, World Scientific 2008, 131 - 141
The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs (with C. G. Jockusch, Jr., B. Kjos-Hanssen, S. Lempp, and T. A. Slaman), in Chong, Feng, Slaman, Woodin, and Yang (eds.), Computational Prospects of Infinity, Part II: Presented Talks, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 15, World Scientific 2008, 143 - 161
The Atomic Model Theorem and Type Omitting (with R. A. Shore and T. A. Slaman), Transactions of the American Mathematical Society 361 (2009) 5805 - 5837
Finite Self-Information (with R. Weber), Computability 1 (2012) 85 - 98
Characterizing the Strongly Jump-Traceable Sets via Randomness (with N. Greenberg and A. Nies), Advances in Mathematics 231 (2012) 2252 - 2293
On Finitely Presented Expansions of Computably Enumerable Semigroups (with B. Khoussainov), Algebra and Logic 51 (2012) 435 - 444
Counting the Changes of Random Δ⁰₂ Sets (with S. Figueira, J. S. Miller, K. M. Ng, and A. Nies), Journal of Logic and Computation 25 (2015) 1073 - 1089
Categoricity Properties for Computable Algebraic Fields (with K. Kramer, R. Miller, and A. Shlapentokh), Transactions of the American Mathematical Society 367 (2015) 3981 - 4017
Asymptotic Density and the Coarse Computability Bound (with C. G. Jockusch, Jr., T. H. McNicholl, and P. E. Schupp), Computability 5 (2016) 13 - 27
On Notions of Computability-Theoretic Reduction between Π¹₂ Principles (with C. G. Jockusch, Jr.), Journal of Mathematical Logic 16 (2016) 1650002
Coarse Reducibility and Algorithmic Randomness (with C. G. Jockusch, Jr., R. Kuyper, and P. E. Schupp), Journal of Symbolic Logic 81 (2016) 1028 - 1046
Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem (with K. Lange and R. A. Shore), Memoirs of the American Mathematical Society 249 (2017), no. 1187, 101 pp.
The Reverse Mathematics of Hindman's Theorem for Sums of Exactly Two Elements (with B. F. Csima, D. D. Dzhafarov, C. G. Jockusch, Jr., R. Solomon, and L. B. Westrick), Computability 8 (2019) 253 - 263
Dense Computability, Upper Cones, and Minimal Pairs (with E. P. Astor and C. G. Jockusch, Jr.), Computability 8 (2019) 155 - 177
A Minimal Pair in the Generic Degrees, Journal of Symbolic Logic 85 (2020) 531 - 537
Ramsey's Theorem and Products in the Weihrauch Degrees (with D. D. Dzhfarov, J. L. Goh, L. Patey, and A. Pauly), Computability 9 (2020) 85 - 110
Combinatorial Principles Equivalent to Weak Induction (with C. Davis, J. L. Hirst, J. Pardo, A. Pauly, and K. Yokoyama), Computability 9 (2020) 219 - 229
Some Results Concerning the SRT²₂ vs. COH Problem (with P. A. Cholak, D. D. Dzhafarov, and L. Patey), Computability 9 (2020) 193 - 217
Reduction Games, Provability, and Compactness (with D. D. Dzhafarov and S. C. Reitzes), Journal of Mathematical Logic 22 (2022) 2250009
Thin Set Versions of Hindman's Theorem (with Sarah C. Reitzes), to appear in the Notre Dame Journal of Formal Logic
Coarse Computability, the Density Metric, Hausdorff Distances between Turing Degrees, Perfect Trees, and Reverse Mathematics (with C. G. Jockusch, Jr. and P. E. Schupp), submitted