Reverse mathematics of a color basis theorem, with Caleb Davis, Silva Keohulian, Brody Miller, and Jessica Ross, submitted. A draft is available locally.
Banach's theorem in higher order reverse mathematics, with Carl Mummert, Computability, 12 (2023) 203-225. Available online at (DOI) 10.3233/COM-230453 for subscribers or purchase. A pre-review draft is available locally and at arXiv.org. After review, numbering of sections and theorems changed, and the final section was modified.
Reverse mathematics and Weihrauch analysis motivated by finite complexity theory, with Zack BeMent and Asuka Wallace, Computability, 10:4 (2021) 343–354. Available online at (DOI) 10.3233/COM-210310 for subscribers or purchase. A draft is available locally.
Combinatorial principles equivalent to weak induction, with Caleb Davis, Denis Hirschfeldt, Jake Pardo, Arno Pauly, and Keita Yokoyama, Computability, 9:3-4 (2020) 219-229. Available online at (DOI) 10.3233/COM-180244, for subscribers or purchase. A draft is available locally and at arXiv.org.
Leaf management, Computability, 9:3-4 (2020) 309-314. Available online at (DOI) 10.3233/COM-180243z, for subscribers or purchase. A draft is available locally and at arXiv.org.
Using Ramsey's theorem once, with Carl Mummert, Archive for Mathematical Logic, 58 (2019) 857-866. Available online at (DOI) 10.1007/s00153-019-00664-z, for subscribers or purchase. An author accepted manuscript is available locally. This article can be viewed through the Springer Nature Content Sharing Intiative. There is a corrigendum that corrects the first definition.
Reverse mathematics and colorings of hypergraphs with C. Davis, J. Pardo, and T. Ransom, Archive for Mathematical Logic, 58 (2019) 575-585. Available online at (DOI) 10.1007/s00153-018-0654-z, for subscribers or purchase. An author accepted manuscript is available locally. This article can be viewed through the Springer Nature Content Sharing Intiative.
Review of: J. Stillwell, Reverse Mathematics: Proofs from the Inside Out, Princeton University Press, Princeton, 2018, xiii + 182 pp. The Bulletin of Symbolic Logic, 24 (2018) 176--177. Available online (DOI) 10.1017/bsl.2018.19 for individual purchase, subscribers, and members of the ASL.
Reverse mathematics of matroids, with Carl Mummert, in Computability and Complexity, Editors Day, Fellows, Greenberg, Khoussainov, Melnikov, and Rosamond, Lecture Notes in Computer Science 10010 (2017) 143-159. Springer-Verlag. Available online (DOI) 10.1007/978-3-319-50062-1 for purchase. A draft is available locally and at arXiv.org.
Reverse mathematics and marriage problems with finitely many solutions, with Noah Hughes, Archive for Mathematical Logic, 55(7) (2016) 1015--1024. Available online (DOI) 10.1007/s00153-016-0509-4 for subscribers. This article can be viewed through the Springer Nature Content Sharing Intiative. A draft is available.
On uniform relationships between combinatorial problems, with François Dorais, Damir Dzhafarov, Joseph Mileti, and Paul Shafer, Transactions of the American Mathematical Society, 368 (2016) 1321--1359. Available online (DOI) 10.1090/tran/6465 for subscribers. A draft is available.
Comparing the strength of diagonally non-recursive functions in the absence of Σ02 induction, with François Dorais and Paul Shafer, The Journal of Symbolic Logic, 80:4 (2015) 1211--1235. Available online http://journals.cambridge.org/abstract_S0022481215000432 for subscribers. A draft is available.
Review of: Denis R. Hirschfeldt. Slicing the truth: On the computable and reverse mathematics of combinatorial principles. The Bulletin of Symbolic Logic, 21 (2015) 338--339. Available online (DOI) 10.1017/bsl.2015.18 for individual purchase, subscribers, and members of the ASL.
On the existence of a connected component of a graph, with Kirill Gura and Carl Mummert, Computability 4 (2015) 103-117. Available online (DOI) 10.3233/COM-150039 for individual purchase, subscribers, and members of CIE. A draft is available.
Reverse mathematics and marriage problems with unique solutions, with Noah Hughes, Archive for Mathematical Logic 54 (2015) 49-57. Available online (DOI) 10.1007/s00153-014-0401-z for subscribers. A draft is available.
Generics for computable Mathias forcing, with Peter Cholak, Damir Dzhafarov, and Theodore Slaman, Annals of Pure and Applied Logic 165:9 (2014) 1418-1428. Available online (DOI) 10.1016/j.apal.2014.04.011. A draft is available.
Reverse mathematics and algebraic field extensions, with François Dorais and Paul Shafer, Computability 2:2 (2013) 75-92. Available online (DOI) 10.3233/COM-13021. A draft is available.
Disguising induction: Proofs of the pigeonhole principle for trees, in: Foundational Adventures: Essays in Honor of Harvey M. Friedman, (Neil Tennant, editor) Templeton Press (2012). Available online at foundationaladventures.wordpress.com. A draft is available in pdf format.
Reverse mathematics, trichotomy, and dichotomy, with François Dorais and Paul Shafer, Journal of Logic and Analysis 4:13 (2012) 1-14. Available online (DOI) 10.4115/jla.2012.4.13. A draft is available in pdf format.
On Mathias generic sets, with Peter Cholak and Damir Dzhafarov, pages 129-138 in: How the World Computes: Proceedings of the Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, LNCS 7318, (Cooper, Dawar, and Lowe, editors) Springer-Verlag (2012) ISBN: 978-3-642-30869-7. Available online (DOI) 10.1007/978-3-642-30870-3_14. A draft is available in pdf format.
More reverse mathematics of the Heine-Borel theorem, with Jessica Miller, Journal of Logic and Analysis 4:6 (2012) 1-10. Available online (DOI) 10.4115/jla.2012.4.6. A draft is available in pdf format.
Hilbert versus Hindman, Archive for Mathematical Logic 51:1-2 (2012) 123-125. Available online (DOI) 10.1007/s00153-011-0257-4 for subscribers. A draft is available in pdf format.
Reverse mathematics and uniformity in proofs without excluded middle, with Carl Mummert, Notre Dame Journal of Formal Logic 52:2 (2011) 149-162. Available online (DOI) 10.1215/00294527-1306163, for subscribers. A draft is available in pdf format.
Ramsey's theorem for trees: The polarized tree theorem and notions of stability, with Damir Dzhafarov and Tamara Lakins, Archive for Mathematical Logic 49:3 (2010) 399-415. Available online (DOI) 10.1007/s00153-010-0179-6, for subscribers. A draft is available in pdf format.
Partitions of trees and ACA'0, with Bernard Anderson, Archive for Mathematical Logic 48:3 (2009) 227-230. Available online (DOI) 10.1007/s00153-009-0122-x, for subscribers. A draft is available in pdf format.
The polarized Ramsey's theorem, with Damir Dzhafarov, Archive for Mathematical Logic, 48:2 (2009) 141-157. Available online (DOI) 10.1007/s00153-008-0108-0, for subscribers. A draft is available in pdf format. (N.B.: Reference [3] should be 1956 rather than 1965.)
Reverse mathematics, computability, and partitions of trees, with Jennifer Chubb and Timothy McNicholl, Journal of Symbolic Logic, 74 (2009) 201-215. A reprint is available in pdf format. (N.B.: Reference [2] is incorrect. It should be Deuber, Promel, and Voight's A canonical partition theorem for chains in regular trees, in Combinatorial Theory, Springer Lecture Notes in Mathematics, Volume 969, (1982) pages 115-132.)
Combinatorics and Graph Theory, Second Edition with J. Harris and M. Mossinghoff, Springer-Verlag, New York, (2008). Series: Undergraduate Texts in Mathematics, ISBN 978-0-387-79710-6. A list of errata appears on this web page.
Representations of reals in reverse mathematics, Bulletin of the Polish Academy of Sciences, Mathematics, 55 (2007) 303-316. Available online for subscribers. A reprint is available in pdf format.
Reverse mathematics of separably closed sets, Archive for Mathematical Logic, 65 (2006) 1-2. Available online. A draft is available in pdf format.
A survey of the reverse mathematics of ordinal arithmetic, Reverse Mathematics 2001, Stephen G. Simpson, editor, Lecture Notes in Logic, 21, Association for Symbolic Logic, La Jolla, California (2005) 222-234. A draft is available in pdf format.
Reverse mathematics and ordinal suprema, Reverse Mathematics 2001, Stephen G. Simpson, editor, Lecture Notes in Logic, 21, Association for Symbolic Logic, La Jolla, California (2005) 235-243. A draft is available in pdf format.
A note on compactness of countable sets, Reverse Mathematics 2001, Stephen G. Simpson, editor, Lecture Notes in Logic, 21, Association for Symbolic Logic, La Jolla, California (2005) 219-221. A draft is available in pdf format.
Free sets and reverse mathematics, with P. Cholak, M. Giusto, and C. Jockusch, Reverse Mathematics 2001, Stephen G. Simpson, editor, Lecture Notes in Logic, 21 Association for Symbolic Logic, La Jolla, California (2005) 104-119. A draft is available in pdf format.
Venn diagrams and reasoning, with W. Hutch Sprunt, The Centroid, 31 (2005) 11-16.
Hindman's theorem, ultrafilters, and reverse mathematics, Journal of Symbolic Logic, 69 (2004) 65-72. Available online DOI 10.2178/jsl/1080938825, for subscribers. Also available from JSTOR at www.jstor.org/stable/30041707. A draft is available in pdf format.
Minima of initial segments of infinite sequences of reals, Mathematical Logic Quarterly, 50 (2004) 47-50. Available online: DOI 10.1002/malq.200310075 (November 2003), for subscribers.
Delivering Web-based Quizzes in Precalculus with WebCT, Proceedings of the 13th annual ICTCM (Atlanta, GA, November 2000). Editor: Goodell, pages 179-181. A draft is available in pdf format.
Reverse mathematics and rank functions for directed graphs, Archive for Mathematical Logic, 39 (2000) 569-579. Available online DOI 10.1007/s001530050165, for subscribers. A draft is available in pdf format.
Combinatorics and Graph Theory, with J. Harris and M. Mossinghoff, Springer-Verlag, New York, (2000). Series: Undergraduate Texts in Mathematics, ISBN 0-387-98736-3.
A graphical tool for analysis courses, in: Electronic Proceedings of the Eleventh Annual International Conference on Technology in Collegiate Mathematics , Editors: Bogacki, Fife, and Husch (1999).
Ordinal inequalities, transfinite induction, and reverse mathematics, Journal of Symbolic Logic, 64 (1999) 769-774.
Reverse mathematics of prime factorization of ordinals, Archive for Mathematical Logic, 38 (1999) 195-201.
Reverse mathematics and recursive graph theory, with W. Gasarch, Mathematical Logic Quarterly, 44 (1998) 465-473. (A earlier version of this paper can be obtained from the Mathematics ArXiv.)
Reverse mathematics and ordinal multiplication, Mathematical Logic Quarterly, 44 (1998) 459-464.
Incorporating Modeling into Undergraduate Courses, with H. Hirst, in Proceedings of the International Conference on the Teaching of Mathematics (University of the Aegean, Samos, Greece), John Wiley and Sons, Inc., (1998) 149-151.
Reverse mathematics of some topics from algorithmic graph theory, with P. Clote, Fundamenta Mathematicae, 157 (1998) 1-13.
Infinite versions of some problems from finite complexity theory, with S. Lempp, Notre Dame Journal of Formal Logic, 37:4 (1996) 545-553. (A version of this paper can be obtained from Mathematics ArXiv.)
Animators in the classroom, in: Electronic Proceedings of the Ninth Annual International Conference on Technology in Collegiate Mathematics , Editors: Bogacki, Fife, and Husch (1996).
A graphical tool for linear algebra,, with William Bauldry, MapleTech, 3 (1996) 48-49. (More information about the Maple procedure eshow.)
Reverse mathematics and ordinal exponentiation, The Annals of Pure and Applied Logic, 66 (1994) 1-18.
Derived sequences and reverse mathematics, Mathematical Logic Quarterly, 39 (1993) 447-453. (DOI) 10.1002/malq.19930390148
Embeddings of countable closed sets and reverse mathematics, Archive for Mathematical Logic, 32 (1993) 443-449.
Connected components of graphs and reverse mathematics, Archive for Mathematical Logic, 31 (1992) 183-192. (DOI) 10.1007/BF01269946
Reverse mathematics of homeomorphic embeddings, with H. Friedman, The Annals of Pure and Applied Logic, 54 (1991) 229-253.
Weak comparability of well orderings and reverse mathematics, with H. Friedman, The Annals of Pure and Applied Logic, 47 (1990) 11-29.
Marriage theorems and reverse mathematics, Logic and Computation, Contemporary Mathematics 106, American Mathematical Society, 1990, 181-196.
Logical analysis of some theorems of combinatorics and topological dynamics, with A. Blass and S. Simpson, Logic and Combinatorics, Contemporary Mathematics 65, American Mathematical Society, 1987, 125-156.
Combinatorics in subsystems of second order arithmetic, Ph.D. Thesis, Pennsylvania State University, 1987. (Available in pdf format.)
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