*Formal Consistency Proofs and Interpretability of Theories*. PhD thesis, University of California, Berkeley, July 1957.- Degrees of unsolvability associated with classes of formalized
theories,
*J. Symbolic Logic*, vol. 22, pp. 161-175, 1957. - (with R. L. Vaught), The first order properties of products of
algebraic systems,
*Fund. Math.*, vol. 47, pp. 57-103, 1959. - (with A. Ehrenfeucht), Representability of recursively
enumerable sets in formal theories,
*Arch. Math. Logik Grundlagenforsch.*, vol. 5, pp. 37-41, 1959. - Arithmetization of metamathematics in a general setting,
*Fund. Math.*, vol. 49, pp. 35-92, 1960. - (with G. Kreisel and S. Orey), 1-consistency and faithful
interpretations,
*Arch. Math. Logik Grundlagenforsch.*, vol. 5, pp. 52-63, 1960. - Classifications of recursive functions by means of
hierarchies,
*Trans. Amer. Math. Soc.*, vol. 104, pp. 101-122, 1962. - Transfinite recursive progressions of axiomatic theories,
*J. Symbolic Logic*, vol. 27, pp. 259-316, 1962. - (with C. Spector), Incompleteness along paths in progressions
of theories,
*J. Symbolic Logic*, vol. 27, pp. 383-390, 1962. - Systems of predicative analysis,
*J. Symbolic Logic*, vol. 29, pp. 1-30, 1964. - Some applications of the notions of forcing and generic sets
(Summary), in
*The Theory of Models,*(Proc. 1963 Internat. Sympos., Berkeley), pp. 89-95, North-Holland, Amsterdam, 1965. - Some applications of the notions of forcing and generic sets,
*Fund. Math.*, vol. 56, pp. 325-345, 1965. *The Number Systems. Foundations of Algebra and Analysis*.

Addison-Wesley, Reading, xii + 418 pp., 1964.- (with G. Kreisel), Persistent and invariant formulas relative
to theories of higher order, (Research Announcement)
*Bull. Amer. Math. Soc.*, vol. 72, pp. 480-485, 1966. - Predicative provability in set theory, (Research
Announcement)
*Bull. Amer. Math. Soc.*, vol. 72, pp. 486-489, 1966. - Systems of predicative analysis, II. Representations of
ordinals,
*J. Symbolic Logic*, vol. 33, pp. 193-220, 1968. - Autonomous transfinite progressions and the extent of
predicative mathematics, in
*Logic, Methodology, and Philosophy of Science III,*(Proc. 3rd Internat. Congr., Amsterdam, 1967), pp. 121-135, North-Holland, Amsterdam, 1968. - Persistent and invariant formulas for outer extensions,
*Compositio Math.*, vol. 20, pp. 29-52, 1968. - Lectures on proof theory, in
*Proceedings of the Summer School in Logic,*(Leeds, 1967), Lecture Notes in Mathematics, vol. 70, pp. 1-107, Springer-Verlag, Berlin, 1968. - Hereditarily replete functionals over the ordinals, in
*Intuitionism and Proof Theory,*(Proc. Conf., Buffalo, 1968), pp. 289-301, North-Holland, Amsterdam, 1970. - Formal theories for transfinite iterations of generalized
inductive definitions and some subsystems of analysis, in
*Intuitionism and Proof Theory,*(Proc. Conf., Buffalo, 1968), pp. 303-326, North-Holland, Amsterdam, 1970. - Set-theoretical foundations of category theory, in
*Reports of the Midwest Category Seminar, III,*Lecture Notes in Mathematics, vol. 106, pp. 201-247, Springer-Verlag, Berlin, 1969.

(with an Appendix by G. Kreisel). - Predicatively reducible systems of set theory, in
*Axiomatic Set Theory,*Proc. Sympos. in Pure Math. vol. XIII, Part 2, pp. 11-32, Amer. Math. Soc., Providence, 1974. - Ordinals and functionals in proof theory, in
*Actes du Congrès International des Mathématiciens (Nice) 1970,*vol. 1, pp. 229-233, Gauthier-Villars, Paris, 1971. - Infinitary properties, local functors, and systems of ordinal
functions, in
*Conference in Mathematical Logic - London '70,*Lecture Notes in Mathematics, vol. 255, pp. 63-97, Springer-Verlag, Berlin, 1972. - Applications of many-sorted interpolation theorems, in
*Proceedings of the Tarski Symposium,*Proc. Sympos. in Pure Math., vol. XXV, pp. 205-223, Amer. Math. Soc., Providence, 1974. - Intuitionism (part of an article on ``Mathematics, foundations
of''), in
*Encyclopedia Britannica*, 15th ed. pp. 633-635 and p. 639, 1974. - Two notes on abstract model theory. I. Properties invariant on
the range of definable relations between structures,
*Fund. Math.*, vol. 82, pp. 153-165, 1974. - Two notes on abstract model theory. II. Languages for which
the set of valid sentences is semi-invariantly implicitly
definable,
*Fund. Math.*, vol. 89, pp. 111-130, 1975. - Recursion in total functionals of finite type,
*Compositio Math.*, vol. 35, pp. 3-22, 1977. - A language and axioms for explicit mathematics, in
*Algebra and Logic,*Lecture Notes in Mathematics, vol. 450, pp. 87-139, Springer-Verlag, Berlin, 1975. - A more perspicuous formal system for predicativity, in
*Konstruktionen versus Positionen, I*, pp. 68-93, Walter de Gruyter, Berlin, 1979. - Impredicativity of the existence of the largest divisible
subgroup of an Abelian p-group, in
*Model Theory and Algebra. A Memorial Tribute to A. Robinson,*Lecture Notes in Mathematics, vol. 498, pp. 117-130, Springer-Verlag, Berlin, 1975. - Non-extensional type-free theories of partial operations and
classifications, I, in
*Proof Theory Symposion, Kiel, 1974,*Lecture Notes in Mathematics, vol. 500, pp. 73-118, Springer-Verlag, Berlin, 1975. - Generating schemes for partial recursively continuous
functionals (summary), in
*Colloque International de Logique,*(Clermont-Ferrand, 1975), pp. 191-198, Èditions du C.N.R.S., Paris, 1977. - Theories of finite type related to mathematical practice, in
*Handbook of Mathematical Logic*, pp. 913-971, North-Holland, Amsterdam, 1977. - Categorical foundations and foundations of category theory, in
*Logic, Foundations of Mathematics and Computability Theory,*(Proc. 5th Internat. Cong. Logic, Methodology, and Philosophy of Science, London, Ont., 1975), vol. 1, pp. 149-169, Reidel, Dordrecht, 1977. - Generalizing set-theoretical model theory and an analogue
theory on admissible sets, in
*Essays on Mathematical and Philosophical Logic,*Synthese Library, vol. 22, pp. 171-195, Reidel, Dordrecht, 1979. - Review of
*Proof Theory*by G. Takeuti,*Bull. Amer. Math. Soc.*, vol. 83, pp. 351-361, 1977. - Inductive schemata and recursively continuous functionals, in
*Logic Colloquium '76*(Proc. Oxford Conference), pp. 373-392, North-Holland, Amsterdam, 1977. - Recursion theory and set theory: a marriage of convenience, in
*Generalized Recursion Theory II*, pp. 55-98, North-Holland, Amsterdam, 1978. - Review of
*Proof Theory*by K. Schütte,*Bull. (New Series) Amer. Math. Soc.*, vol. 1, pp. 224-228, 1979. - What does logic have to tell us about mathematical proofs?,
*The Mathematical Intelligencer*, vol. 2, pp. 20-24, 1979. - Constructive theories of functions and classes, in
*Logic Colloquium '78,*(Proc. Mons Colloq.), pp. 159-224, North-Holland, Amsterdam, 1979. - The logic of mathematical discovery vs. the logical structure
of mathematics, in
*PSA 1978*, pp. 309-327, Philosophy of Science Assoc., East Lansing, 1978. - (with P. Aczel), Consistency of the unrestricted abstraction
principle using an intensional equivalence operator, in
*To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism*, pp. 67-98, Academic Press, New York, 1980. - Progressões transfinitas recursivas de teorias
axiomáticas (translation of ``Transfinite recursive
progressions of axiomatic theories''), in
*O Teorema de Gödel e a Hipótese do Contínuo*, pp. 573-754, Fundacão C. Gulbenkian, Lisbon, 1979. - As progressões tranfinitas autónomas e a
extensão da matemática predicativa (translation of
``Autonomous transfinite progressions and the extent of
predicative mathematics''), in
*O Teorema de Gödel e a Hipótese do Contínuo*, pp. 755-790, Fundacão C. Gulbenkian, Lisbon, 1979. - Sistemas de análise predicativa (translation of
``Systems of predicative analysis''), in
*O Teorema de Gödel e a Hipótese do Contínuo*, pp. 790-866, Fundacão C. Gulbenkian, Lisbon, 1979. - (with W. Buchholz, W. Pohlers, and W. Sieg),
*Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-theoretical Studies,*Lecture Notes in Mathematics, vol. 897, 388 pps.

Springer-Verlag, Berlin, 1981. - How we got from there to here, in
*Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-theoretical Studies,*Lecture Notes in Mathematics, vol. 897, pp. 1-15, Springer-Verlag, Berlin, 1981.

(Preface). - (with W. Sieg), Iterated inductive definitions and subsystems
of analysis, in
*Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-theoretical Studies,*Lecture Notes in Mathematics, vol. 897, pp. 16-77, Springer-Verlag, Berlin, 1981. - (with W. Sieg), Proof-theoretic equivalences between classical
and constructive theories for analysis, in
*Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-theoretical Studies,*Lecture Notes in Mathematics, vol. 897, pp. 78-142, Springer-Verlag, Berlin, 1981. - Iterated inductive fixed-point theories: application to
Hancock's conjecture, in
*Patras Logic Symposion*, pp. 171-196, North-Holland, Amsterdam, 1982. - Inductively presented systems and the formalization of
meta-mathematics, in
*Logic Colloquium '80*, pp. 95-128, North-Holland, Amsterdam, 1982. - A theory of variable types,
*Revista Colombiana de Matématicas,*(Proc. Latin Amer. Logic Symp., Bogotá 1981), vol. 19, pp. 95-105, 1985. - Monotone inductive definitions, in
*The L. E. J. Brouwer Centenary Symposium*, pp. 77-89, North-Holland, Amsterdam, 1982. - (with G. Jäger), Choice principles, the bar rule and
autonomously iterated comprehension schemes in analysis,
*J. Symbolic Logic*, vol. 48, pp. 63-70, 1983. - Toward useful type-free theories, I,
*J. Symbolic Logic*, vol. 49, pp. 75-111, 1984. - Working foundations,
*Synthese*, vol. 62, pp. 229-254, 1985. - Foundational ways, in
*Perspectives in Mathematics*, pp. 147-158, Birkhäuser, Basel, 1984. - Kurt Gödel: conviction and caution,
*Philosophia Naturalis*, vol. 21, pp. 546-562, 1984. - Between constructive and classical mathematics, in
*Computation and Proof Theory,*Lecture Notes in Mathematics, vol. 1104, pp. 143-162, Springer Verlag, Berlin, 1984. - Intensionality in mathematics,
*J. Philosophical Logic*, vol. 14, pp. 41-55, 1985. - (with J. Barwise, eds.),
*Model-theoretic Logics,*xviii + 893 pp.

Springer-Verlag, Berlin, 1985. - (with J.W. Dawson, Jr., S. C. Kleene, G. H. Moore, R. M.
Solovay, and J. van Heijenoort, eds.),
*Kurt Gödel. Collected Works, Vol. I. Publications 1929-1936*.

Oxford Univ. Press, New York, xvi + 474 pp., 1986. - Gödel's life and work, in
*Kurt Gödel. Collected Works, Vol. I. Publications 1929-1936*, pp. 1-36, Oxford Univ. Press, New York, 1986. - Proof theory: a personal report, Appendix to
*Proof Theory,*2nd edn., by G. Takeuti, pp. 447-485, North-Holland, Amsterdam, 1987. - Infinity in mathematics: is Cantor necessary?, in
*L'infinito nella scienza (Infinity in Science)*, pp. 151-209, Istituto della Enciclopedia Italiana, Rome, 1987. - Hilbert's program relativized: proof-theoretical and
foundational reductions,
*J. Symbolic Logic*, vol. 53, pp. 364-384, 1988. - Turing in the land of 0(
*z*), in*The Universal Turing Machine. A Half-century Survey*, pp. 113-147, Oxford Univ. Press, Oxford, 1988. - Weyl vindicated:
*Das Kontinuum*70 years later, in*Temi e prospettive della logica e della filosofia della scienza contemporanee, vol. I*, pp. 59-93, CLUEB, Bologna, 1988. - Polymorphic typed lambda-calculi in a type-free axiomatic
framework, in
*Logic and Computation,*Comtemporary Mathematics, vol. 106, pp. 101-136, Amer. Math. Soc., Providence, 1990. - Finitary inductively presented logics, in
*Logic Colloquium '88*, pp. 191-220, North Holland, Amsterdam, 1989; reprinted in*What is a Logical System?*(D. S. Gabbay, ed.), Clarendon Press, Oxford (1994), 297-328. - Kurt Gödel: conviction and caution, reprinting in
*Gödel's Theorem in Focus*, pp. 96-114, Croom Helm, London, 1988. *The Number Systems. Foundations of Algebra and Analysis,*2nd ed.

Chelsea Pub. Co., New York, xii + 418 pp., 2nd ed., 1989.- (with J.W. Dawson, Jr., S. C. Kleene, G. H. Moore, R. M.
Solovay, and J. van Heijenoort, eds.),
*Kurt Gödel. Collected Works, Vol. II, Publications 1938-1974*.

Oxford Univ. Press, New York, xv + 407 pp., 1990. - Reflecting on incompleteness,
*J. Symbolic Logic*, vol. 56, pp. 1-49, 1991. - Logics for termination and correctness of functional programs,
in
*Logic from Computer Science*, pp. 95-127, MSRI Pubs. vol. 21, Springer-Verlag, New York, 1992. - Logics for termination and correctness of functional programs,
II. Logics of strength PRA, in
*Proof Theory*(Leeds Proof Theory Programme 1990), pp. 197-225, Cambridge University Press, Cambridge, 1993. - Turing's `Oracle': From absolute to relative computability -
and back, in
*The Space of Mathematics*, pp. 314-348, Walter de Gruyter, Berlin, 1992. - Proofs of termination and the ``91'' function, in
*Artificial Intelligence and Mathematical Theory of Computation. Papers in honor of John McCarthy*, pp. 47-63, Academic Press, Boston, 1991. - Working foundations - `91, in
*Bridging the Gap: Philosophy, Mathematics and Physics,*Boston Studies in the Philos. of Science vol. 140, pp. 99-124, Kluwer, Dordrecht, 1993. - A new approach to abstract data types, I. Informal
development,
*Mathematical Structures in Computer Science*, vol. 2, pp. 193-229, 1992. - A new approach to abstract data types, II. Computability on
ADTs as ordinary computation, in
*Computer Science Logic,*Lecture Notes in Computer Science vol. 626, pp. 79-95, Springer-Verlag, Berlin, 1992. - Jean van Heijenoort's scholarly work, Appendix to
*Politics, Logic and Love. The Life of Jean van Heijenoort,*by A.B. Feferman, pp. 371-390, A. K. Peters Ltd., Wellesley, 1993. - The development of programs for the foundations of mathematics
in the first third of the 20th century.

To appear in*Storia del XX secolo: Logica*, Istituto della Enciclopedia Italiana, Rome. - Julia Bowman Robinson, December 8, 1919 - July 30, 1985.

*Biographical Memoirs of the National Academy of Sciences*63, 453-478, 1994. - What rests on what? The proof-theoretic analysis of
mathematics, in
*Philosophy of Mathematics*, Part I, pp. 147-171, Proceedings of the 15th International Wittgenstein Symposium, Verlag Hölder-Pichler-Tempsky, Vienna, 1993. - Why a little bit goes a long way: Logical foundations of
scientifically applicable mathematics, in
*PSA 1992*, Vol. II, 442-455, 1993. - (with G. Hellman), Predicative foundations of arithmetic.
*J. Philosophical Logic*24, 1-17, 1995. - (with G. Jäger), Systems of explicit mathematics with
non-constructive -operator.
Part I.

*Annals of Pure and Applied Logic*65, 243-263, 1993. - Gödel's
*Dialectica*interpretation and its two-way stretch, in*Computational Logic and Proof Theory*, Lecture Notes in Computer Science 713, 23-40, 1993. - (with J.W. Dawson, Jr., W. Goldfarb, C. Parsons, and R.M.
Solovay, eds.),
*Kurt Gödel. Collected Works, Vol. III, Unpublished essays and lectures*.

Oxford Univ. Press, 1995. - (with G. Jäger), Systems of explicit mathematics with
non-constructive -operator.
Part II,
*Annals of Pure and Applied Logic*79, 37-52, 1996. - Ordinal logics,
*The Cambridge Dictionary of Philosophy*, 550-551, 1995. - Reflection principles,
*The Cambridge Dictionary of Philosophy*, 682, 1995. - Ordinal logics (entry in the
*Routledge Encyclopedia of Philosophy*). - Kreisel's ``unwinding'' program, in
*Kreiseliana*. A.K. Peters Ltd. 1996, 247-273. - Deciding the undecidable: Wrestling with Hilbert's Problems. (Inaugural address, Stanford, May 13, 1994; Ch.1 in item 109).
- Penrose's Gödelian argument, PSYCHE 2 (1996), 21-32.
- Definedness,
*Erkenntnis*43, 295-320, 1995. - Computation on abstract data types. The extensional approach,
with an application to streams,
*Annals of Pure and Applied Logic*, 81 (1996) 75-113. - Proof theory, to appear in
*Encyclopedia of Philosophy Supplement*, MacMillan Pub. Co. - Gödel's program for new axioms: Why, where, how and
what?, in
*Gödel '96*, Lecture Notes in Logic 6 (1996), 3-22. - (Editor)
*The Collected Works of Julia Robinson*, American Mathematical Society (1996). - (with G. Hellman) Challenges to predicative foundations of
arithmetic. in G. Sher and R. Tieszen, eds.,
*Between Logic and Intuition: Essays in Honor of Charles Parsons*, Kluwer Academic Publishers (1999) 317-339 - (with T. Strahm) The unfolding of non-finitist arithmetic.
*Annals of Pure and Applied Logic*104 (2000), 75-96. *In the Light of Logic*. Oxford University Press, 1998, xii + 340 pp.- Does mathematics need new axioms?,
*Amer. Math. Monthly*106 (1999), 99-111. - My route to arithmetization.
*Theoria 63(1997)*, 168-181. - (with J. Avigad) Gödel's functional ("Dialectica")
interpretation, in
*The Handbook of Proof Theory*(S. Buss, ed.), North-Holland Pub. Co. (1998) 337-405. - Three conceptual problems that bug me. (Lecture text for 7th Scandinavian Logic Symposium, 1996).
- Tarski and Gödel between the lines, in
*Tarski and the Vienna Circle*(J. Wolenski and E. Köhler, eds.), Kluwer Academic Publishers (1998), 53-63. - Highlights in proof theory, in
*Proof Theory*(V.F. Hendricks et al., eds.), Kluwer Academic Publishers (2000), 11-31. - The significance of Hermann Weyl's
*Das Kontinuum*,*ibid*., 179-194. - Relationships between constructive, predicative and classical
systems of analysis,
*ibid*., 221-236. - Mathematical intuition vs. mathematical monsters.
*Synthese*125 (2000), 317-332. - Ah, Chu. In
*JFAK. Essays Dedicated to Johan van Benthem on the Occasion of his Fiftieth Birthday*, Amsterdam Univ. Press (1999), CD-ROM only. - Logic, logics, and logicism.
*Notre Dame J. of Formal*40 (1999), 31-54.*Logic* - Does reductive proof theory have a viable rationale?
*Erkenntnis*53 (2000), 63-96. - Alfred Tarski and a watershed conference 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. - Does mathematics need new axioms? (Proceedings of a
symposium), with Harvey M. Friedman, Penelope Maddy, and John. R.
Steel.
*Bull. of Symbolic Logic*6 (2000) 401-446. - Why the programs for new axioms need to be questioned. (In
preceding item.)
*Bull. Symbolic Logic*6, 401-413. - In memoriam: Kenneth Jon Barwise, 1942-2000.
*Bull. Symbolic Logic*6 (2000) 505-508. - Tarski's conception of logic.
*Annals of Pure and Applied Logic*126 (2004) 5-13. - 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. - Predicativity.
*The Oxford Handbook of the Philosophy of Mathematics and Logic*(S. Shapiro ed.), Oxford University Press, Oxford (2005) 590-624. *Kurt Gödel. Collected Works. Vol. IV. Correspondence A-G (*as editor-in-chief, with J. W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Wilfried Sieg, co-editors). Oxford University Press (Oxford), 2003.*Kurt Gödel. Collected Works. Vol. V. Correspondence H-Z*(as editor-in-chief, with J. W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Wilfried Sieg, co-editors). Oxford University Press (Oxford), 2003.- 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) 131-151. - What kind of logic is "Independence Friendly" logic?, in
*The Philosophy of Jaakko Hintikka (*Randall E. Auxier and Lewis E. Hahn, eds.), Library of Living Philosophers, Open Court (2006), 453-469. - 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. - The Gödel editorial project: A synopsis,
*Bull. Symbolic Logic*11 (2005) 132-149. - 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. - Are there absolutely unsolvable problems? Gödel's
dichotomy,
*Philosophia Mathematica*(2006) 14(2): 134-152. - Review of
*Incompleteness. The proof and paradox of Kurt Gödel,*by Rebecca Goldstein,*London Review of Books*vol. 28 no. 3 (9 Feb. 2006). - The impact of the incompleteness theorems on mathematics,
*Notices of the American Mathematical Society*53, no.4 (April 2006), 434-439. - Turing's thesis,
*Notices American Mathematical Society,*53 no. 10 (Nov. 2006), 1200-1205. - Lieber Herr Bernays! Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's program,
*Dialectica*62 (2008), 179-203. (This is a preprint of the following; the differences are of an editorial nature.) - Lieber Herr Bernays! Lieber Herr Gödel! Gödel on finitism, constructivity and Hilbert's program, in (M. Baaz, et al., eds.)
*Kurt Gödel and the Foundations of Mathematics. Horizons of Truth,*Cambridge Univ. Press, Cambridge (2011), 111-133. - Harmonious logic: Craig's interpolation theorem and its descendants,
*Synthese*164, no. 3 (2008), 341-357. - Axioms for determinateness and truth,
*The Review of Symbolic Logic*1, no. 2 (2008), 204-217. - Philosophy of Mathematics: 5 questions, in (V. F. Hendricks and H. Leitgeb, eds.)
*Philosophy of Mathematics: 5 Questions*, Automatic Press/VIP (2008) 115-135. - Gödel, Nagel, minds and machines,
*J. of Philosophy*CVI no. 4 (2009), 201-219. (Ernest Nagel Lecture, Columbia University, Sept. 27, 2007). - Operational set theory and small large cardinals,
*Information and Computation*207 (2009), 971-979. - Modernism in mathematics, review of
*Plato's Ghost*by Jeremy Gray,*American Scientist*97 no. 5 (2009), 417. - Conceptions of the continuum,
*Intellectica*51 (2009), 169-189. - The unfolding of finitist arithmetic (with Thomas Strahm),
*The Review of Symbolic Logic*3 (2010), 665-689. - Set-theoretical invariance criteria for logicality,
*Notre Dame J. of Formal Logic*51 (2010), 3-20. - Gödel's incompleteness theorems, free will and mathematical thought, in (R. Swinburne, ed.)
*Free Will and Modern Science*, Oxford Univ. Press for the British Academy, Oxford (2011), 102-122. - On the strength of some semi-constructive theories, in (S. Feferman and W. Sieg, eds.)
*Proof, Categories and Computation: Essays in Honor of Grigori Mints*, College Publications, London (2010), 109-129; reprinted in (U. Berger, et al., eds.)*Logic, Construction, Computation*, Ontos Verlag, Frankfurt (2012), 201-22. - 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. (Wolfram Pohlers Festschrift volume). - Axiomatizing truth: Why and how, in (U. Berger, et al., eds.)
*Logic, Construction, Computation*, Ontos Verlag, Frankfurt (2012), 185-200. (Helmut Schwichtenberg Festschrift volume.) - And so on ... Reasoning with infinite diagrams,
*Synthese*186 (2012), 371-386. - Review of Curtis Franks,
*The Autonomy of Mathematical Knowledge. Hilbert's program revisited,*in*Philosophia Mathematica. Series III*, 20 no. 3 (2012), 387-400. - On rereading van Heijenoort's
*Selected Essays*, in*Logica Universalis*6 no. 3-4 (2012), 535-552. - Foundations of unlimited category theory: What remains to be done,
*The Review of Symbolic Logic*6 (2013), 6-15. - How a little bit goes a long way: Predicative foundations of analysis, http://math.stanford.edu/~feferman/papers/pfa(1).pdf, unpublished notes dating from 1977-1981, with a new introduction.
- About and around computing over the reals, in (B. J. Copeland, C. J. Posy and O. Shagrir, eds.)
*Computability. Turing, Gödel, Church, and Beyond*, MIT Press (2013), 55-76. - Turing's Thesis: Ordinal logics and oracle computability, in
*Alan Turing: His Work and Impact*(S. B. Cooper and J. van Leeuwen, eds.) Elsevier, Amsterdam (2013), 145-150.