(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. Two notes on abstract model theory. I. Properties invariant on the range of definable relations between structures, Fundamenta Mathematicae 82 (1974) 153-165.
11. 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.
12. Choice principles, the bar rule, and autonomously iterated comprehension schemes in analysis (with G. Jäger), J. Symbolic Logic 48 (1983), 63-70.
13. Toward useful type-free theories, I, J. Symbolic Logic 49 (1984), 75-111.
14. Hilbert's program relativized: Proof-theoretical and foundational reductions, J. Symbolic Logic 53 (1988), 364-384.
15. Finitary inductively presented logics, in Logic Colloquium '88 (R. Ferro, et al., eds.), North-Holland, Amsterdam (1989) 191-220.
16. Reflecting on incompleteness, J. Symbolic Logic 56 (1991), 1-49.
17. 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.
18. 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.
19. 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.
20. Predicative foundations of arithmetic (with G. Hellman), J. Philosophical Logic 24 (1995) 1-17.
21. 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.
22. Kreisel's "unwinding" program, in Kreiseliana (P. Odifreddi, ed.), A. K. Peters Ltd., Wellesley (1996) 247-273.
23. 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.
24. Penrose's Gödelian argument, PSYCHE 2 (1996) 21-32.
25. Definedness, Erkenntnis 43 (1995) 295-320.
26. Computation on abstract data types. The extensional approach, with an application to streams, Annals of Pure and Applied Logic 81 (1996) 75-113.
27. Proof Theory Since 1960, prepared for the Encyclopedia of Philosophy Supplement, Macmillan Publishing Co., New York.
28. 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.
29. 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.
30. The unfolding of non-finitist arithmetic (with T. Strahm), Annals of Pure and Applied Logic 104 (2000) 75-96.
31. Does mathematics need new axioms?, American Mathematical Monthly 106 (1999) 99-111.
32. My route to arithmetization, Theoria 63 (1997) 168-181.
33. 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.
34. Three conceptual problems that bug me, Unpublished lecture text for 7th Scandinavian Logic Symposium, Uppsala, 1996.
35. Highlights in Proof Theory, in Proof Theory (V. F. Hendricks, et al., eds.) Kluwer Academic Publishers, Dordrecht (2000) 11-31.
36. The significance of Hermann Weyl's Das Kontinuum, ibid., 179-194.
37. Relationships between Constructive, Predicative and Classical Systems of Analysis, ibid., 221-236.
38. Mathematical Intuition vs. Mathematical Monsters, Synthese 125 (2000) 317-332.
39. 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.
40. Logic, Logics, and Logicism, Notre Dame J. of Formal Logic 40 (1999) 31-54.
41. Does reductive proof theory have a viable rationale?, Erkenntnis 53 (2000) 63-96.
42. 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.
43. 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.
44. Tarski's conception of logic, Annals of Pure and Applied Logic 126 (2004) 5-13.
45. Tarski's conceptual analysis of semantical notions, Sémantique et épistémologie (A. Benmakhlouf, ed.) Editions Le Fennec, Casablanca (2004) [distrib. J. Vrin, Paris] 79-108.
46. 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).
47. Predicativity. In The Oxford Handbook of Philosophy of Mathematics and Logic (S. Shapiro, ed.), Oxford University Press, Oxford (2005) 590-624.
48. 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.
49. 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.
50. 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.
51. 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.
52. The Gödel editorial project: a synopsis Bull. Symbolic Logic 11 (2005) 132-149.
53. Enriched stratified systems for the foundations of category theory, in What is Category Theory? (G. Sica, ed.), Polimetrica, Milano (2006), 185-203.
54. 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).
55. Review of Incompleteness. The proof and paradox of Kurt Gödel, by Rebecca Goldstein, London Review of Books, vol. 28, no. 3 (9 February 2006).
56. The impact of Gödel's incompleteness theorems on mathematics, Notices American Mathematical Society 53 no. 4 (April 2006), 434-439.
57. Are there absolutely unsolvable problems? Gödel's dichotomy, Philosophia Mathematica, Series III vol. 14 (2006), 134-152.
58. Turing's thesis, Notices American Mathematical Society 53 no. 10 (Nov. 2006), 1200-1205.
59. Operational set theory and small large cardinals (draft 12/05/06)
60. The nature and significance of Gödel's incompleteness theorems, lecture for the Princeton Institute for Advanced Study Gödel Centenary Program, Nov. 17, 2006.
61. Lieber Herr Bernays! Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's program, submitted version of lecture for the Gödel centenary conference, Horizons of Truth, Vienna, 27-29 April 2006.
62. 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.
63. Axioms for determinateness and truth, The Review of Symbolic Logic, August 2008.
64. Philosophy of mathematics: 5 questions, in Philosophy of Mathematics: 5 Questions (V. F. Hendricks and H. Leitgeb, eds.), Automatic Press/VIP 2008, 115-135.
65. Gödel, Nagel, minds and machines, Ernest Nagel Lecture, Columbia University, Sept. 27, 2007.
66. Harmonious logic: Craig's , Synthese, October 2008.
67. 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.
68. Conceptual structuralism and the continuum, lecture slides for an invited talk at VIII International Ontology Congress, San Sebastian, October 1, 2008.
69. Conceptions of the continuum, talk at Barcelona Workshop on the Foundations of Mathematics, October 6, 2008.
70. 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.