Solomon Feferman--Papers and Slides in PDF Format

(Caveat lector: published versions of the following may contain some changes.)

  1. Degrees of unsolvability associated with classes of formalized theories, J. Symbolic Logic 22 (1957) 161-175.
  2. The first order properties of products of algebraic systems (with R. L. Vaught), Fundamenta Mathematicae 47 (1959), 57-103.
  3. Arithmetization of metamathematics in a general setting, Fundamenta Mathematicae 49 (1960),35-92.
  4. Transfinite recursive progressions of axiomatic theories, J. Symbolic Logic 27 (1962), 259-316.
  5. Incompleteness along paths in progressions of theories (with C. Spector), J. Symbolic Logic 27 (1962), 383-390.
  6. Classifications of recursive functions by means of hierarchies, Transactions Amer. Math. Soc. 104 (1962), 101-122.
  7. Systems of predicative analysis, J. Symbolic Logic 29 (1964), 1-30.
  8. Some applications of the notions of forcing and generic sets, Fundamenta Mathematicae 56 (1965), 325-345.
  9. Systems of predicative analysis, II. Representation of ordinals, J. Symbolic Logic 33 (1968), 193-220.
  10. Persistent and invariant formulas for outer extensions, Compositio Mathematica 20 (1968), 29-52.
  11. Two notes on abstract model theory. I. Properties invariant on the range of definable relations between structures, Fundamenta Mathematicae 82 (1974) 153-165.
  12. Two notes on abstract model theory. II. Languages for which the set of valid sentences is semi-invariantly implicitly definable, Fundamenta Mathematicae 89 (1975) 111-130.
  13. A language and axioms for explicit mathematics, in Algebra and Logic (J. N. Crossley, ed.), Lecture Notes in Mathematics 450 (1975), 87-139.
  14. Categorical foundations and foundations of category theory, in R.E. Butts and J. Hintikka, eds., Logic, Foundations of Mathematics, and Computability Theory, Reidel, Dordrecht (1977) 149-169.
  15. Recursion in total functionals of finite type, Compositio Mathematica 35 (1977), 3-22.
  16. Recursion theory and set theory: A marriage of convenience, in Generalized Recursion Theory II (J. E. Fenstad, et al., eds.), North-Holland (1978), 55-98.
  17. Constructive theories of functions and classes, in Logic Colloquium '78 (M. Boffa, et al., eds.), North-Holland (1979), 159-224.
  18. Choice principles, the bar rule, and autonomously iterated comprehension schemes in analysis (with G. Jäger), J. Symbolic Logic 48 (1983), 63-70.
  19. Toward useful type-free theories, I, J. Symbolic Logic 49 (1984), 75-111.
  20. A theory of variable types, Rivista Columbiana de Matemáticas XIX (1985), 95-105.
  21. Hilbert's program relativized: Proof-theoretical and foundational reductions, J. Symbolic Logic 53 (1988), 364-384.
  22. Finitary inductively presented logics, in Logic Colloquium '88 (R. Ferro, et al., eds.), North-Holland, Amsterdam (1989) 191-220; reprinted in What is a Logical System? (D. S. Gabbay, ed.), Clarendon Press, Oxford (1994), 297-328.
  23. Reflecting on incompleteness, J. Symbolic Logic 56 (1991), 1-49.
  24. The development of programs for the foundations of mathematics in the first third of the 20th century. (1993). Appears in translation as "Le scuole de filosofia della matematica" in Storia della scienza (S. Petruccioli, ed.) Istituto della Enciclopedia Italiana, 10 v., 2001-2004, v. VIII (2004) 112-121.
  25. Systems of explicit mathematics with non-constructive mu-operator, Part I (with G. Jäger), Annals of Pure and Applied Logic 65 (1993), 243-263.
  26. Systems of explicit mathematics with non-constructive mu-operator, Part II (with G. Jäger), Annals of Pure and Applied Logic 79 (1996), 37-52.
  27. What rests on what? The proof-theoretic analysis of mathematics, in Philosophy of Mathematics Part I (J. Czermak, ed.) Proc. of the 15th International Wittgenstein Symposium, Verlag Hölder-Pichler-Tempsky, Vienna (1993) 141-171; reprinted as Ch. 10 in In the Light of Logic, Oxford Univ. Press, New York (1998) 187-208.
  28. Why a little bit goes a long way: Logical foundations of scientifically applicable mathematics, in PSA 1992, Vol. II, 442-455, 1993. Reprinted as Chapter 14 in In the Light of Logic, 284-298.
  29. Predicative foundations of arithmetic (with G. Hellman), J. Philosophical Logic 24 (1995) 1-17.
  30. Godel's Dialectica interpretation and its two-way stretch, in Computational Logic and Proof Theory (G. Gottlob, et al., eds.), Lecture Notes in Computer Science 713 (1993) 23-40; reprinted as Ch. 11 in In the Light of Logic, 209-225.
  31. Kreisel's "unwinding" program, in Kreiseliana (P. Odifreddi, ed.), A. K. Peters Ltd., Wellesley (1996) 247-273.
  32. Deciding the Undecidable: Wrestling with Hilbert's Problems, Inaugural address, Stanford Univ., May 13, 1994, published as Ch. 1 in In the Light of Logic, 3-27.
  33. Penrose's Gödelian argument, PSYCHE 2 (1996) 21-32.
  34. Definedness, Erkenntnis 43 (1995) 295-320.
  35. Computation on abstract data types. The extensional approach, with an application to streams, Annals of Pure and Applied Logic 81 (1996) 75-113.
  36. Proof Theory Since 1960, prepared for the Encyclopedia of Philosophy Supplement, Macmillan Publishing Co., New York.
  37. Gödel's program for new axioms: Why, where, how and what?, in Gödel '96 (P. Hajek, ed.), Lecture Notes in Logic 6 (1996), 3-22.
  38. Challenges to predicative foundations of arithmetic (with G. Hellman), in Between Logic and Intuition. Essays in Honor of Charles Parsons (G. Sher and R. Tieszen, eds.), Cambridge Univ. Press, Cambridge (2000) 317-338.
  39. The unfolding of non-finitist arithmetic (with T. Strahm), Annals of Pure and Applied Logic 104 (2000) 75-96.
  40. Does mathematics need new axioms?, American Mathematical Monthly 106 (1999) 99-111.
  41. My route to arithmetization, Theoria 63 (1997) 168-181.
  42. Godel's Functional ("Dialectica") Interpretation (with J. Avigad), in The Handbook of Proof Theory (S. Buss, ed.), North-Holland Pub. Co., Amsterdam (1998) 337-405.
  43. Three conceptual problems that bug me, Unpublished lecture text for 7th Scandinavian Logic Symposium, Uppsala, 1996.
  44. Highlights in Proof Theory, in Proof Theory (V. F. Hendricks, et al., eds.) Kluwer Academic Publishers, Dordrecht (2000) 11-31.
  45. The significance of Hermann Weyl's Das Kontinuum, ibid., 179-194.
  46. Relationships between Constructive, Predicative and Classical Systems of Analysis, ibid., 221-236.
  47. Mathematical Intuition vs. Mathematical Monsters, Synthese 125 (2000) 317-332.
  48. Ah, Chu, in JFAK. Essays Dedicated to Johan van Benthem on the Occasion of his Fiftieth Birthday, Amsterdam Univ. Press, Amsterdam (1999), CD-ROM only.
  49. Logic, Logics, and Logicism, Notre Dame J. of Formal Logic 40 (1999) 31-54.
  50. Does reductive proof theory have a viable rationale?, Erkenntnis 53 (2000) 63-96.
  51. Alfred Tarski and a watershed meeting in logic: Cornell, 1957 , in (J. Hintikka, et al., eds.) Philosophy and Logic. In search of the Polish tradition, Synthese Library vol. 323, Kluwer Acad. Pubs. (2003), 151-162.
  52. Does mathematics need new axioms?, (Proceedings of a symposium with H. M. Friedman, P. Maddy and J. Steel, Bulletin of Symbolic Logic 6 (2000) 401-413.
  53. Tarski's conception of logic, Annals of Pure and Applied Logic 126 (2004) 5-13.
  54. Tarski's conceptual analysis of semantical notions, Sémantique et épistémologie (A. Benmakhlouf, ed.) Editions Le Fennec, Casablanca (2004) [distrib. J. Vrin, Paris] 79-108. Reprinted in (D. Patterson, ed.) New Essays on Tarski and Philosophy, Oxford Univ. Press (2008), 72-93.
  55. Notes on Operational Set Theory I. Generalization of "small" large cardinals in classical and admissible set theory, draft (Theorem 4(i), p. 5, needs correction).
  56. Predicativity. In The Oxford Handbook of Philosophy of Mathematics and Logic (S. Shapiro, ed.), Oxford University Press, Oxford (2005) 590-624.
  57. Typical ambiguity. Trying to have your cake and eat it too. One Hundred Years of Russell's Paradox (G. Link, ed.), Walter de Gruyter, Berlin (2004) 135-151.
  58. Some formal systems for the unlimited theory of functors and categories. Unpublished MS from 1972-73 referred to in the preceding paper, sec. 8. Uneven scanning has resulted in some missing symbols that can be restored according to context, including: p. 18, l.6, S*; p.19, Theorem 3.1, S*, and p.26, l.3, a epsilon* b.
  59. What kind of logic is "Independence Friendly" logic?, in The Philosophy of Jaakko Hintikka (Randall E. Auxier and Lewis Edwin Hahn, eds.); Library of Living Philosophers vol. 30, Open Court (2006), 453-469.
  60. Comments on "Predicativity as a philosophical position" by G. Hellman, Review Internationale de Philosophie (special issue, Russell en héritage. Le centenaire des Principles, Ph. de Rouilhan, ed.) 229 (no. 3, 2004), 313-323.
  61. The Gödel editorial project: a synopsis Bull. Symbolic Logic 11 (2005) 132-149; reprinted in Kurt Gödel. Essays for his Centennial (S. Feferman, C. Parsons and S. G. Simpson, eds.), Lecture Notes in Logic 33 (2010), Assoc. for Symbolic Logic, Cambridge University Press, 2010.
  62. Enriched stratified systems for the foundations of category theory, in What is Category Theory? (G. Sica, ed.), Polimetrica, Milano (2006), 185-203;  reprinted in (G. Sommaruga, ed.), Foundational Theories of Classical and Constructive Mathematics, Springer, Dordrecht (2011), 127-143.
  63. Tarski's influence on computer science, invited lecture for LICS 2005, Chicago, June 28, 2005. Has appeared in Logical Methods in Computer Science, vol. 2 issue 3 (2006).
  64. Review of Incompleteness. The proof and paradox of Kurt Gödel, by Rebecca Goldstein, London Review of Books, vol. 28, no. 3 (9 February 2006).
  65. The impact of Gödel's incompleteness theorems on mathematics, Notices American Mathematical Society 53 no. 4 (April 2006), 434-439.
  66. Are there absolutely unsolvable problems? Gödel's dichotomy, Philosophia Mathematica, Series III vol. 14 (2006), 134-152.
  67. Turing's thesis, Notices American Mathematical Society 53 no. 10 (Nov. 2006), reprinted in Alan Turing's Systems of Logic. The Princeton Thesis (A. W. Appel, ed.), Princeton Univ. Press, 13-26.
  68. The nature and significance of Gödel's incompleteness theorems, lecture for the Princeton Institute for Advanced Study Gödel Centenary Program, Nov. 17, 2006.
  69. Lieber Herr Bernays! Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's , in Kurt Gödel and the Foundations of Mathematics. Horizons of Truth (M. Baaz, et al., eds.) Cambridge University Press (2011), 111-133.
  70. Lieber Herr Bernays! Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's program, preprint of the preceding in Dialectica 62 (2008), 179-203. (With some editorial differences.)
  71. Harmonious logic: Craig's interpolation theorem and its descendants, transparencies for the lecture at Interpolations--A Conference in Honor of William Craig, UC Berkeley, 13 May 2007.
  72. Harmonious logic: Craig's interpolation theorem and its descendants, Synthese 164, no. 3 (2008), 341-357.
  73. Axioms for determinateness and truth, The Review of Symbolic Logic, 1 no. 2 (2008), 204-217.
  74. Philosophy of mathematics: 5 questions, in Philosophy of Mathematics: 5 Questions (V. F. Hendricks and H. Leitgeb, eds.), Automatic Press/VIP 2008, 115-135.
  75. Gödel, Nagel, minds and machines, Ernest Nagel Lecture, Columbia University, Sept. 27, 2007; J. Philosophy CVI, nr. 4, April 2009, 201-219.
  76. The Proof Theory of Classical and Constructive Inductive Definitions: A 40 year saga, slides for an invited talk at the Pohlersfest, Münster 18 July 2008.
  77. Conceptual structuralism and the continuum, slides for talk Phil Math Intersem 2010 Université Paris 7-Diderot, 6/08/10 (revision of slides for talk at VIIIth International Ontology Congress, San Sebastián, 10/01/08).
  78. Conceptions of the continuum, slides for talk at Barcelona Workshop on the Foundations of Mathematics, October 6, 2008.
  79. And so on ...: Reasoning with infinite diagrams, slides for talk at Workshop on Diagrams in Mathematics, Paris, October 9, 2008, and Logic Seminar, Stanford, February 24, 2009.
  80. What's definite? What's not? Slides for talk at Harvey Friedman 60th birthday conference, Ohio State U., May 16, 2009.
  81. On the strength of some semi-constructive theories, in Proof, Categories and Computation: Essays in honor of Grigori Mints, (S. Feferman and W. Sieg, eds.), College Publications, London (2010), 109-129; reprinted in Logic, Construction, Computation (U. Berger, et al., eds.)(H. Schwichtenberg Festschrift volume), Ontos Verlag, Frankfurt (2012), 201-225.
  82. The proof theory of classical and constructive inductive definitions. A 40 year saga, 1968-2008, in (R. Schindler, ed.) Ways of Proof Theory, Ontos Verlag, Frankfurt (2010), 7-30.
  83. Operational set theory and small large cardinals, Information and Computation 207 (2009), 971-979.
  84. Modernism in mathematics, review of Plato's Ghost by Jeremy Gray (Princeton U. Press, 2008), American Scientist 97 no. 5 (Sept-Oct 2009), 417.
  85. Conceptions of the continuum, Intellectica 51 (2009/1), 169-189.
  86. The unfolding of finitist arithmetic (with Thomas Strahm), The Review of Symbolic Logic 3 (2010), 665-689.
  87. Set-theoretical invariance criteria for logicality, Notre Dame J. of Formal Logic 51 (2010), 3-20.
  88. Gödel's incompleteness theorems, free will and mathematical thought, in Free Will and Modern Science (R. Swinburne, ed.), OUP for the British Academ (2011), 102-122.
  89. Foundations of category theory: What remains to be done, slides for contributed talk at ASL 2011 meet, UC Berkeley, March 24, 2011.
  90. Axiomatizing Truth: How and Why , slides for invited lecture at Pillars of Truth Conference, Princeton University, April 8-10, 2011.
  91. Axiomatizing truth: Why and how, in Logic, Construction, Computation (U. Berger, et al., eds.)(H. Schwichtenberg Festschrift volume), Ontos Verlag, Frankfurt (2012) 185-200.
  92. About and around computing over the reals, to appear in Computability: Gödel, Church, Turing and Beyond (J. Copeland, C. Posy and O. Shagrir, eds), MIT Press.
  93. Which quantifiers are logical?: A combined semantical and inferential criterion, slides for talk Aug 08, 2011, ESSLLI Workshop on Logical Constants, Ljubljana.
  94. Which quantifiers are logical? A combined semantical and inferential criterion, text for preceding talk; to appea in Synthese..
  95. Is the Continuum Hypothesis a definite mathematical problem?, Draft of paper for the lecture to the Philosophy Dept., Harvard University, Oct. 5, 2011 in the EFI project series.
  96. Is the Continuum Hypothesis a definite mathematical problem?, slides for the preceding talk.
  97. Turing's 'Oracle': From absolute to relative computability--and back, slides for Logic Seminar talk, Stanford, April 10, 2012.
  98. About and around computing over the reals, slides for Logic Seminar talk, Stanford, April 17, 2012.
  99. And so on... Reasoning with infinite diagrams, Synthese 186, no. 1 (2012), 371-386.
  100. Review of Curtis Franks The Autonomy of Mathematical Knowledge. Hilbert's program revisited, Philosophia Mathematica. Series III, 20 no.3 (2012), 387-400.
  101. On rereading van Heijenoort's Selected Essays, Logica Universalis 6 no. 3-4 (2012), 535-552.
  102. Introduction to Foundations of Explicit Mathematics (book in progress by S. Feferman, G. Jäger, S.Strahm, with the assistnace of U. Buchholtz), draft 7/19/12.
  103. Three Problems for Mathematics; Lecture 1: Bernays, Gödel, and Hilbert's consistency program, slides for inaugural Paul Bernays Lectures, ETH, Zurich, Sept. 11, 2012.
  104. Three Problems for Mathematics: Lecture 2: Is the Continuum Hypothesis a definite mathematical problem?, slides for inaugural Paul Bernays Lectures, ETH, Zurich, Sept. 12, 2012.
  105. Three Problems for Mathematics; Lecture 3: Foundations of Unlimited Category Theory, slides for inaugural Paul Bernays Lectures, ETH, Zurich, Sept. 12, 2012.
  106. What's special about mathematical proofs?, Remarks for the Williams Symposium on Proof, University of Pennsylvania, Nov. 9, 2012.
  107. Foundations of unlimited category theory: What remains to be done, The Review of Symbolic Logic 6 (2013), 6-15.
  108. Why isn't the Continuum Problem on the Millennium ($1,000,000) Prize list?, slides for CSLI Workshop on Logic, Rationality and Intelligent Interaction, Stanford, June 1, 2013.
  109. How a little bit goes a long way: Predicative foundations of analysis, unpublished notes dating from 1977-1981, with a new introduction.
  110. Theses for computation and recursion on concrete and abstract structures, to appear in a Turing Centennial volume for Birkhäuser edited by G. Sommaruga and T. Strahm.
  111. Categoricity and open-ended axiom systems, lecture slides for the conference, "Intuition and Reason", in honor of Charles Parsons, Tel-Aviv, Dec. 2, 2013; full YouTube video.
  112. The operational perspective, lecture slides for the conference, "Advances in Proof Theory 2013" in honor of Gerhard Jäger, Bern, Dec. 14, 2013.
  113. Logic, mathematics and conceptual structuralism, in The Metaphysics of Logic (P. Rush, ed.), Cambridge University Press, 2014 (to appear).
  114. A fortuitous year with Leon Henkin, to appear in The Life and Work of Leon Henkin--Essays on his Contributions (M. Manzano, I. Sain and E. Alonso, eds.), Springer International.,
  115. The Continuum Hypothesis is neither a definite mathematical problem nor a definite logical problem, revised version of 2011 Harvard Philos. Dept. EFI lecture.