Publication List

Stephen G. Simpson Vanderbilt University Pennsylvania State University www.math.psu.edu/simpson sgslogic@gmail.com

February 22, 2021

(Abstracts and technical reports are not included.)

[1] Gerald E. Sacks and Stephen G. Simpson, The α-finite injury method, Annals of Mathematical Logic, 4, 1972, pp. 343–367.

[2] Stephen G. Simpson, Admissible Ordinals and Recursion Theory, Ph. D. Thesis, Massachusetts Institute of Technology, 1971, 107 pages.

[3] Manuel Lerman and Stephen G. Simpson, Maximal sets in α-recursion theory, Israel Journal of Mathematics, 4, 1973, pp. 236–247.

[4] Stephen G. Simpson, Degree theory on admissible ordinals, in: Generalized Recursion Theory, edited by J.-E. Fenstad and P. G. Hinman, North-Holland, Amsterdam, 1974, pp. 165–194.

[5] Stephen G. Simpson, Post’s problem for admissible sets, in: Generalized Recursion Theory, edited by J.-E. Fenstad and P. G. Hinman, North-Holland, Amsterdam, 1974, pp. 437–441.

[6] Stephen G. Simpson, Minimal covers and hyperdegrees, Transactions of the American Mathematical Society, 209, 1975, pp. 45–64.

[7] Carl G. Jockusch, Jr., and Stephen G. Simpson, A degree theoretic definition of the ramified analytical hierarchy, Annals of Mathematical Logic, 10, 1976, pp. 1–32.

[8] Stephen G. Simpson, Forcing and models of arithmetic, Proceedings of the American Mathematical Society, 43, 1974, pp. 193–194.

[9] Stephen G. Simpson, Notes on subsystems of analysis (informally distributed lecture notes), typewritten and mimeographed, Berkeley, 1973, 38 pages.

[10] Stephen G. Simpson, Degrees of unsolvability: a survey of results, in: Handbook of Mathematical Logic, edited by J. Barwise, North-Holland, Amsterdam, 1977, pp. 631–652.

[11] Stephen G. Simpson, Sets which do not have subsets of every higher degree, Journal of Symbolic Logic, 43, l978, pp. 135–138.

[12] Stephen G. Simpson, Basis theorems and countable admissible ordinals, Actes du Colloque de Logique de Clermont-Ferrand (July 1975), 1978, pp. 161–165.

[13] Stephen G. Simpson, First order theory of the degrees of recursive unsolvability, Annals of Mathematics, 105, 1977, pp. 121–139.

[14] Stephen G. Simpson, Short course on admissible recursion theory, in: Generalized Recursion Theory II, edited by J.-E. Fenstad, R. O. Gandy and G. E. Sacks, North-Holland, Amsterdam, 1978, pp. 355–390.

[15] Karel Hrbaček and Stephen G. Simpson, On Kleene degrees of analytic sets, in: Kleene Symposium, edited by J. Barwise, H. J. Keisler and K. Kunen, North-Holland, Amsterdam, 1980, pp. 347–352.

[16] Stephen G. Simpson, The hierarchy based on the jump operator, in: Kleene Symposium, edited by J. Barwise, H. J. Keisler and K. Kunen, North-Holland, Amsterdam, 1980, pp. 267–276.

[17] Stephen G. Simpson, BQO theory and Fraïsse’s Conjecture, Chapter 9 of: Recursive Aspects of Descriptive Set Theory, by R. B. Mansfield and G. Weitkamp, Oxford University Press, New York, 1985, pp. 124–138.

[18] Stephen G. Simpson, Four test problems in generalized recursion theory, in: Proceedings of the Sixth International Congress on Logic, Methodology and Philosophy of Science, North-Holland, Amsterdam, 1982, pp. 263–270.

[19] James Schmerl and Stephen G. Simpson, On the role of Ramsey quantifiers in first order arithmetic, Journal of Symbolic Logic, 47, 1982, pp. 15–27.

[20] Harvey Friedman, Kenneth McAloon and Stephen G. Simpson, A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis, in: Patras Logic Symposion, edited by G. Metakides, North-Holland, Amsterdam, 1982, pp. 197–220.

[21] Alain Louveau and Stephen G. Simpson, A separable image theorem for Ramsey mappings, Bulletin de la Académie Polonaise des Sciences, Série Mathematique, 20, 1982, pp. 105–108.

[22] Stephen G. Simpson and Galen Weitkamp, High and low Kleene degrees of coanalytic sets, Journal of Symbolic Logic, 47, 1982, pp. 356–368.

[23] Stephen G. Simpson, Σ_{1}^{1} and Π_{1}^{1} transfinite induction, in: Logic Colloquium ’80, edited by D. van Dalen, D. Lascar and J. Smiley, North-Holland, Amsterdam, 1982, pp. 239–253.

[24] Stephen G. Simpson, Set theoretic aspects of ATR_{0}, in: Logic Colloquium ’80, edited by D. van Dalen, D. Lascar and J. Smiley, North-Holland, Amsterdam, 1982, pp. 255–271.

[25] Stephen G. Simpson, Which set existence axioms are needed to prove the Cauchy/Peano theorem of ordinary differential equations?, Journal of Symbolic Logic, 49, 1984, pp. 783–802.

[26] Timothy J. Carlson and Stephen G. Simpson, A dual form of Ramsey’s Theorem, Advances in Mathematics, 53, 1984, pp. 265–290.

[27] Harvey Friedman, Stephen G. Simpson, and Rick Smith, Countable algebra and set existence axioms, Annals of Pure and Applied Logic, 25, 1983, pp. 141–181; Addendum, 28, 1985, pp. 320–321.

[28] Stephen G. Simpson, Reverse Mathematics, in: Recursion Theory, edited by A. Nerode and R. A. Shore, Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Number 42, 1985, pp. 461–471.

[29] Stephen G. Simpson and Rick Smith, Factorization of polynomials and Σ_{1}^{0} induction, Annals of Pure and Applied Logic, 31, 1986, pp. 289–306.

[30] Stephen G. Simpson, Nichtbeweisbarkeit von gewissen kombinatorischen Eigenschaften endlicher Bäume, Archiv für mathematische Logik und Grundlagen der Mathematik, 25, 1985, pp. 45–65.

[31] Stephen G. Simpson, Recursion theoretic aspects of the dual Ramsey theorem, in: Recursion Theory Week, Oberwolfach, 1984, Proceedings, edited by H.-D. Ebbinghaus, G. H. Müller and G. E. Sacks, Lecture Notes in Mathematics, Number 1141, Springer-Verlag, Heidelberg, 1986, pp. 356–371.

[32] Kurt Schütte and Stephen G. Simpson, Ein in der reinen Zahlentheorie unbeweisbarer Satz über endlichen Folgen von natürlichen Zahlen, Archiv für mathematische Logik und Grundlagen der Mathematik, 25, 1985, pp. 75–89.

[33] Heinz-Jürgen Prömel, Stephen G. Simpson, and Bernd Voigt, A dual form of Erdős-Radó’s canonization lemma, Journal of Combinatorial Theory, Series A, 42, 1986, pp. 159–178.

[34] Stephen G. Simpson, Friedman’s research on subsystems of second order arithmetic, in: [42], 1985, pp. 137–159.

[35] Stephen G. Simpson, Subsystems of Z_{2} and Reverse Mathematics, appendix to: Proof Theory, second edition, by G. Takeuti, North-Holland, Amsterdam, 1987, pp. 432–446.

[36] Stephen G. Simpson, Nonprovability of certain combinatorial properties of finite trees (English translation of [30]), in: [42], 1985, pp. 87–117.

[37] Timothy J. Carlson and Stephen G. Simpson, Topological Ramsey Theory, in: Mathematics of Ramsey Theory, edited by J. Nesetřil and V. Rödl, Springer-Verlag, 1990, pp. 172–183.

[38] Douglas K. Brown and Stephen G. Simpson, Which set existence axioms are needed to prove the separable Hahn-Banach Theorem?, Annals of Pure and Applied Logic, 31, 1986, pp. 123–144.

[39] Stephen G. Simpson, Partial realizations of Hilbert’s Program, Journal of Symbolic Logic, 53, 1988, pp. 349–363.

[40] Andreas Blass, Jeffry L. Hirst, and Stephen G. Simpson, Logical analysis of some theorems of combinatorics and topological dynamics, in: [43], pp. 125–156.

[41] Stephen G. Simpson, Unprovable theorems and fast-growing functions, in: [43], pp. 359–394.

[42] Leo Harrington, Michael Morley, Andre Ščedrov and Stephen G. Simpson (editors), Harvey Friedman’s Research in the Foundations of Mathematics, North-Holland, Amsterdam, 1985, XVI + 408 pages.

[43] Stephen G. Simpson (editor), Logic and Combinatorics, Contemporary Mathematics, Number 65, American Mathematical Society, 1987, XI + 394 pages.

[44] Stephen G. Simpson, Ordinal numbers and the Hilbert Basis Theorem, Journal of Symbolic Logic, 53, 1988, pp. 961–974.

[45] Kostas Hatzikiriakou and Stephen G. Simpson, Countable valued fields in weak subsystems of second order arithmetic, Annals of Pure and Applied Logic, 41, 1989, pp. 27–32.

[46] Kostas Hatzikiriakou and Stephen G. Simpson, WKL_{0} and orderings of countable Abelian groups, in: Logic and Computation, edited by W. Sieg, Contemporary Mathematics, Number 106, American Mathematical Society, 1990, pp. 177–180.

[47] Xiaokang Yu and Stephen G. Simpson, Measure theory and weak König’s lemma, Archive for Mathematical Logic, 30, 1990, pp. 171–180.

[48] Harvey Friedman, Stephen G. Simpson and Xiaokang Yu, Periodic points in subsystems of second order arithmetic, Annals of Pure and Applied Logic, 62, 1993, pp. 51–64.

[49] Douglas K. Brown and Stephen G. Simpson, The Baire category theorem in weak subsytems of second order arithmetic, Journal of Symbolic Logic, 58, 1993, pp. 557–578.

[50] Stephen G. Simpson, On the strength of König’s duality theorem for countable bipartite graphs, Journal of Symbolic Logic, 59, 1994, pp. 113– 123.

[51] Ju Rao and Stephen G. Simpson, Reverse algebra, in: Handbook of Recursive Mathematics, edited by Yu. L. Ershov, S. S. Goncharov, A. Nerode, and J. B. Remmel, associate editor V. Marek, volume 2, Recursive Algebra, Analysis, and Combinatorics, Elsevier, 1998, pp. 1355– 1372.

[52] A. James Humphreys and Stephen G. Simpson, Separable Banach space theory needs strong set existence axioms, Transactions of the American Mathematical Society, 348, 1996, pp. 4231–4255.

[53] Douglas K. Brown, Mariagnese Giusto, Stephen G. Simpson, Vitali’s theorem and WWKL, Archive for Mathematical Logic, 41, 2002, pp. 191–206.

[54] Stephen G. Simpson, Finite and countable additivity, 8 pages, draft, November 1996; in preparation.

[55] A. James Humphreys and Stephen G. Simpson, Separation and weak König’s lemma, Journal of Symbolic Logic, 64, 1999, pp. 268–278.

[56] Mariagnese Giusto and Stephen G. Simpson, Located sets and reverse mathematics, Journal of Symbolic Logic, 65, 2000, pp. 1451–1480.

[57] Stephen G. Simpson, Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, 1999, XIV + 445 pages.

[58] Stephen G. Simpson, Logic and mathematics, in: The Examined Life, Readings from Western Philosophy from Plato to Kant, edited by S. Rosen, Random House, 2000, XXVIII + 628 pages, pp. 577–605.

[59] Harvey Friedman and Stephen G. Simpson, Issues and problems in Reverse Mathematics, in: Computability Theory and Its Applications: Current Trends and Open Problems, edited by P. A. Cholak, S. Lempp, M. Lerman and R. A. Shore, Contemporary Mathematics, Number 257, American Mathematical Society, 2000, pp. 127–144.

[60] Stephen G. Simpson, Predicativity: the outer limits, in Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman, edited by W. Sieg, R. Sommer, and C. Talcott, Lecture Notes in Logic, Number 15, Association for Symbolic Logic, 2001, pp. 134–140.

[61] Stephen G. Simpson, Kazuyuki Tanaka, and Takeshi Yamazaki, Some conservation results on weak König’s lemma, Annals of Pure and Applied Logic, 118, 2002, pp. 87–114.

[62] Stephen G. Simpson, Π_{1}^{0} sets and models of WKL_{0}, in: [64], 2005, pp. 352–378.

[63] Stephen G. Simpson, A symmetric β-model, 7 pages, preprint, May 2000, submitted for publication.

[64] Stephen G. Simpson (editor), Reverse Mathematics 2001, Lecture Notes in Logic, Number 21, Association for Symbolic Logic, 2005, X + 401 pages.

[65] Stephen Binns and Stephen G. Simpson, Embeddings into the Medvedev and Muchnik lattices of Π_{1}^{0} classes, Archive for Mathematical Logic, 43, 2004, pp. 399–414.

[66] Stephen G. Simpson, Mass problems and randomness, Bulletin of Symbolic Logic, 11, 2005, pp. 1–27.

[67] Stephen G. Simpson and Theodore A. Slaman, Medvedev degrees of Π_{1}^{0} subsets of 2^{ω}, 4 pages, draft, July 2001; in preparation.

[68] Carl Mummert and Stephen G. Simpson, An incompleteness theorem for β_{n}-models, Journal of Symbolic Logic, 69, 2004, pp. 612–616.

[69] Natasha L. Dobrinen and Stephen G. Simpson, Almost everywhere domination, Journal of Symbolic Logic, 69, 2004, pp. 914–922.

[70] Stephen G. Simpson, Mass problems, lecture notes from the Summer School and Workshop on Proof Theory, Computation and Complexity, held at the Technical University of Dresden, June 23 – July 4, 2003; preprint, 24 pages, 24 May 2004; submitted for publication.

[71] Stephen G. Simpson, An extension of the recursively enumerable Turing degrees, Journal of the London Mathematical Society, 75, 2007, pp. 287– 297.

[72] Carl Mummert and Stephen G. Simpson, Reverse mathematics and Π_{2}^{1} comprehension, Bulletin of Symbolic Logic, 11, 2005, pp. 526–533.

[73] Stephen G. Simpson, Subsystems of Second Order Arithmetic, Second Edition, Perspectives in Logic, Association for Symbolic Logic, 2009, XVI + 444 pages.

[74] Stephen G. Simpson, Some fundamental issues concerning degrees of unsolvability, in: Computational Prospects of Infinity, Part II: Presented Talks, edited by C.-T. Chong, Q. Feng, T. Slaman, H. Woodin, and Y. Yang, Number 15 in Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, World Scientific, 2008, pp. 313–332.

[75] Stephen G. Simpson, Almost everywhere domination and superhighness, Mathematical Logic Quarterly, 53, 2007, pp. 462–482.

[76] Stephen G. Simpson, Mass problems and almost everywhere domination, Mathematical Logic Quarterly, 53, 2007, pp. 483–492.

[77] Joshua A. Cole and Stephen G. Simpson, Mass problems and hyperarithmeticity, Journal of Mathematical Logic, 7, 2008, pp. 125–143.

[78] Stephen G. Simpson, Medvedev degrees of 2-dimensional subshifts of finite type, Ergodic Theory and Dynamical Systems, 34, 2014, pp. 665– 674, http://dx.doi.org/10.1017/etds.2012.152.

[79] Stephen G. Simpson, Mass problems and intuitionism, Notre Dame Journal of Formal Logic, 49, 2008, pp. 127–136.

[80] Stephen G. Simpson, The Gödel hierarchy and reverse mathematics, in [81], 2010, pages 109–127.

[81] Solomon Feferman, Charles Parsons, and Stephen G. Simpson (editors), Kurt Gödel: Essays for his Centennial, Association for Symbolic Logic, Cambridge University Press, 2010, VIII + 373 pages.

[82] Stephen G. Simpson, Częściowe realizacje programu Hilberta, translation of [39], in Współczesna Filozofia Mathematyki, Wybór Tekstów, edited by R. Murawski, translation, introduction and footnotes by Roman Murawski, Wydawnictwo Naukowe PWN, Warszaw, 2002, pp. 189– 213.

[83] Stephen G. Simpson, Mass problems and measure-theoretic regularity, Bulletin of Symbolic Logic, 15, 2009, pp. 385–409.

[84] Stephen G. Simpson and Keita Yokoyama, A non-standard counterpart of WWKL, Notre Dame Journal of Formal Logic, 52, 2011, pp. 229–243.

[85] Stephen G. Simpson, Mass problems associated with effectively closed sets, Tohoku Mathematical Journal, 63, 2011, pp. 489–517.

[86] Stephen G. Simpson, Toward objectivity in mathematics, in: Infinity and Truth, edited by C.-T. Chong, Q. Feng, T. A. Slaman and W. H. Woodin, IMS Lecture Notes Series, Number 25, World Scientific, 2014, pp. 157–169.

[87] Stephen G. Simpson, An objective justification for actual infinity?, in: Infinity and Truth, edited by C.-T. Chong, Q. Feng, T. A. Slaman and W. H. Woodin, IMS Lecture Note Series, Number 25, World Scientific, 2014, pp. 225–228.

[88] Noopur Pathak, Cristóbal Rojas, and Stephen G. Simpson, Schnorr randomness and the Lebesgue differentiation theorem, Proceedings of the American Mathematical Society, 142, 2014, pp. 335–349.

[89] Stephen G. Simpson, Symbolic dynamics: entropy = dimension = complexity, Theory of Computing Systems, 56, 2015, pp. 527–543, http://dx.doi.org/10.1007/s00224-014-9546-8.

[90] Stephen G. Simpson and Keita Yokoyama, Reverse mathematics and Peano categoricity, Annals of Pure and Applied Logic, 164, 2013, pp. 284–293, http://dx.doi.org/10.1016/j.apal.2012.10.014.

[91] Stephen G. Simpson, Baire categoricity and Σ_{1}^{0} induction, Notre Dame Journal of Formal Logic, 55, 2014, pp. 75–78, http://dx.doi.org/10.1215/00294527-2377887.

[92] Kojiro Higuchi, W. M. Phillip Hudelson, Stephen G. Simpson, and Keita Yokoyama, Propagation of partial randomness, Annals of Pure and Applied Logic, 165, 2014, pp. 742–758, http://dx.doi.org/10.1016/j.apal.2013.10.006.

[93] Stephen G. Simpson, Implicit definability in arithmetic, Notre Dame Journal of Formal Logic, 57, 2016, pp. 329–339.

[94] Stephen G. Simpson and Frank Stephan, Cone avoidance and randomness preservation, Annals of Pure and Applied Logic, 166, 2015, pp. 713– 728, http://dx.doi.org/10.1016/j.apal.2015.03.001.

[95] Stephen Binns, Richard A. Shore, and Stephen G. Simpson, Mass problems and density, Journal of Mathematical Logic, 16, 2016, 650006 (10 pages), doi 10.1142/S0219061316500069.

[96] Kostas Hatzikiriakou and Stephen G. Simpson, Reverse mathematics, Young diagrams, and the ascending chain condition, Journal of Symbolic Logic, 82, 2017, pp. 576–589.

[97] Sankha S. Basu and Stephen G. Simpson, Mass problems and intuitionistic higher-order logic, Computability, 5, 2016, pp. 29–47, http://dx.doi.org/10.3233/COM-150041.

[98] Sankha S. Basu and Stephen G. Simpson (translators), Strong and weak reducibility of algorithmic problems, by Albert A. Muchnik, Computability, 5, 2016, pp. 49–59, http://dx.doi.org/10.3233/COM-150042.

[99] Stephen G. Simpson, Degrees of unsolvability: a tutorial, in Evolving Computability, Lecture Notes in Computer Science, Number 9132, Springer, 2015, pp. 83–94.

[100] Stephen G. Simpson, Turing degrees and Muchnik degrees of recursively bounded DNR functions, in Computability and Complexity, Lecture Notes in Computer Science, Number 10010, Springer, 2017, pp. 660–668.

[101] Stephen G. Simpson, Foundations of mathematics: an optimistic message, in: The Legacy of Kurt Schütte, edited by R. Kahle and M. Rathjen, Springer, 2020, pp. 401–414.

[102] Chi Tat Chong and Stephen G. Simpson (guest editors), Special Section: Computability and the Foundation of Mathematics, In Honor of the 60th Birthday of Professor Kazuyuki Tanaka, Annals of the Japan Association for Philosophy of Science, 25, 2017, pp. 23–100.

[103] Hayden Jananthan and Stephen G. Simpson, Pseudojump inversion in special r. b. Π_{1}^{0} classes, 19 pages, submitted for publication February 21, 2020, https://arxiv.org/abs/2102.06135.

[104] Hayden Jananthan and Stephen G. Simpson, Turing degrees of hyperjumps, 19 pages, submitted for publication June 29, 2020, https://arxiv.org/abs/2101.08818.