Publication List

Stephen G. Simpson
simpson@math.psu.edu
http://www.math.psu.edu/simpson/

Pennsylvania State University

June 28, 2017

(Abstracts and technical reports are not included.)

[1] Gerald E. Sacks and Stephen G. Simpson, The alpha-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
    alpha-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 Hrbacek 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 Fraisse'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 Academie Polonaise des
     Sciences, Serie 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, Sigma11 and Pi11 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 ATR0, 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, Number 42, American Mathematical Society, 1985,
     pp. 461-471.
    
[29] Stephen G. Simpson and Rick Smith, Factorization of polynomials
     and Sigma01 induction, Annals of Pure and Applied Logic, 31,
     1986, pp. 289-306.
    
[30] Stephen G. Simpson, Nichtbeweisbarkeit von gewissen
     kombinatorischen Eigenschaften endlicher B"aume, Archiv f"ur
     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. M"uller and
     G. E. Sacks, Lecture Notes in Mathematics, Number 1141,
     Springer-Verlag, Heidelberg, 1986, pp. 356-371.
    
[32] Kurt Sch"utte and Stephen G. Simpson, Ein in der reinen
     Zahlentheorie unbeweisbarer Satz "uber endlichen Folgen von
     nat"urlichen Zahlen, Archiv f"ur mathematische Logik und
     Grundlagen der Mathematik, 25, 1985, pp. 75-89.
    
[33] Heinz-J"urgen Pr"omel, Stephen G. Simpson, and Bernd Voigt, A
     dual form of Erdos-Rado'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 Z2 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. Nesetril
     and V. Rodl, 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 Scedrov 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, l989, pp. 27-32.
    
[46] Kostas Hatzikiriakou and Stephen G. Simpson, WKL0 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
     K"onig'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 K"onig'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, and 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.

[55] A. James Humphreys and Stephen G. Simpson, Separation and Weak
     K"onig'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 K"onig's lemma, Annals of Pure and
     Applied Logic, 118, 2002, pp. 87-114.
  
[62] Stephen G. Simpson, Pi01 sets and models of WKL0, in: [64], 2005,
     pp. 352-378.

[63] Stephen G. Simpson, A symmetric beta-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 Pi01 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
     Pi01 subsets of 2^omega, 4 pages, draft, July 2001; in
     preparation.

[68] Carl Mummert and Stephen G. Simpson, An incompleteness theorem
     for beta_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 Pi12
     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, Lecture Notes Series, Number 15,
     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 G"odel hierarchy and reverse mathematics,
     in [81], 2010, pages 109-127.

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

[82] Stephen G. Simpson, Czesciowe realizacje programu Hilberta,
     translation of [39], in Wspolczesna Filozofia Mathematyki, Wybor
     Tekstow, 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,
     Institute for Mathematical Sciences, National University of
     Singapore, 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, Institute for Mathematical Sciences, National
     University of Singapore, World Scientific, 2014, pp. 225-228.

[88] Noopur Pathak, Cristobal 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/s00224-014-9546-8.30.

[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 Sigma01 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,
     1650006 (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, 11 pages, 20 June 2016, submitted for publication.

[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.