UCI 1999-2000 CHANCELLOR'S DISTINGUISHED FELLOWS SERIES

SOLOMON FEFERMAN

Wednesday, October 20, 1999

*In the Light of Logic*

7:30 p.m.

Social Science Lecture Hall

100

UCI Program Logic & Philosophy Science

Presents

A Colloquium

by

"Where Do Axioms Come From and Where Do They Go?"

Tuesday, October 19, 1999

4pm

775 Social Science Tower"What's the Use of Foundations of Mathematics?"

Thursday, October 21, 1999

4pm

775 Social Science Tower

Compiled by

Eddie Yeghiayan

**Philosophy & Logic & Philosophy of Science Bibliographer**

*The Number Systems: Foundations of Algebra and Analysis*. Addison-Wesley Series in Mathematics. Reading, Mass.: Addison-Wesley, 1964.*The Number Systems: Foundations of Algebra and Analysis*. 2nd edition. New York: Chelsea, 1989.*In the Light of Logic*. Logic and Computation in Philosophy. New York: Oxford University Press, 1998.

__Contents__:

I. Foundational Problems

1. Deciding the Undecidable: Wrestling with Hilbert's Problems

2. Infinity in Mathematics: Is Cantor Necessary?

II. Foundational Ways

3. The Logic of Mathematical Discovery versus the Logical Structure of Mathematics

4. Foundational Ways

5. Working Foundations

III. Gödel

6. Gödel's Life and Work

7. Kurt Gödel: Conviction and Caution

8. Introductory Note to Gödel's 1933 Lecture

IV. Proof Theory

9. What does Logic Have to Tell Us about Mathematical Proofs?

10. What Rests on What? The Proof-Theoretic Analysis of Mathematics

11. Gödel's Dialectica interpretation and its two-way stretch

V. Countably Reducible Mathematics

12. Infinity in Mathematics: Is Cantor Necessary? (Conclusion)

13. Weyl Vindicated: Das Kontinuum Seventy Years later

14. Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics.

Edited with Jon Barwise.

*Model-Theoretic Logics*. Perspectives in Mathematical Logic. New York: Springer-Verlag, 1985.Edited (with J.W. Dawson, Jr., S.C. Kleene, G.H. Moore, R.M. Solovay, and Jean van Heijenoort.) Kurt Gödel's

*Collected Works. Vol. 1: Publications 1929-1936*. Oxford: Clarendon Press; New York: Oxford University Press, 1986.

UCI Science Library QA9 G5313 1986 BarEdited (with J.W. Dawson, Jr., S.C. Kleene, G.H. Moore, R.M. Solovay, and Jean van Heijenoort.) Kurt Gödel's

*Collected Works. Volume II: Publications 1938-1974*. Oxford: Clarendon Press; New York: Oxford University Press, 1990.

UCI Science Library QA9 G5313 1986Edited (with John W. Dawson, Jr., Warren Goldfarb, Charles Parsons and Robert M. Solovay.) Kurt Gödel's

*Collected Works. Volume III: Unpublished Essays and Lectures*. Oxford: Clarendon Press; New York: Oxford University Press, 1995.

UCI Science Library QA9 G5313 1986 BarEdited (with Sergei Artemov, George Boolos, Erwin Engeler, Gerhard Jäger, and Albert Visser.) "Invited papers presented at the Conference on Proof Theory, Provability Logic, and Computation, March 20-24, 1994, Berne, Switzerland." issue of

*Annals of Pure and Applied Logic*(September 12, 1995), 75(1-2).

UCI Science Library BC135 A4 DrumEdited, with a Foreword, Julia Robinson's

*Collected Works*. Providence, RI: American Mathematical Society, 1996.

"Some Applications of the Notions of Forcing and Generic Sets: Summary." In J.W. Addison, Leon Henkin and Alfred Tarski, eds.,

*The Theory of Models: Proceedings*, pp. 89-95. International Symposium on the Theory of Models, 1963, Berkeley, Calif. Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland, 1965.

UCI Main Lib BC135 I586 1963"Autonomous Transfinite Progressions and the Extent of Predicative Mathematics." In B. Van Rootselaar and J. F. Staal, eds.,

*Logic, Methodology and Philosophy of Science III: Proceedings of the Third International Congress for Logic, Methodology and Philosophy of Science, Amsterdam 1967*, pp. 121-135. Amsterdam: North-Holland, 1968.

UCI Science Library Q175 I535 1967 Bar"Lectures on Proof Theory." In M.H. Löb, ed.,

*Proceedings of the Summer School in Logic, Leeds, 1967; N.A.T.O. Advanced Study Institute, Meeting of the Association for Symbolic Logic*, pp. 1-107. Lecture Notes in Mathematics, 70. Berlin & New York: Springer-Verlag, 1968.

UCI Science Library QA3 L28 no. 70 Bar"Set-Theoretical Foundations of Category Theory. (With an Appendix by G. Kreisel." In S. MacLane, ed.,

*Reports of the Midwest Category Seminar III*, pp. 201-247. Lecture Notes in Mathematics, 106. Berlin & New York: Springer, 1969.

UCI Science Library QA3 L28 no. 106 Bar"Formal Theories for Transfinite Iterations of Generalized Inductive Definitions and Some Subsystems of Analysis." In A. Kino, J. Myhill and R. E. Vesley, eds.,

*Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo, N.Y., 1968*, pp. 303-326. Conference on Intuitionism and Proof Theory, 1968, State University of New York at Buffalo. Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland, 1970.

UCI Science Library QA9 C742 1968 Bar"Hereditarily Replete Functionals over the Ordinals." In A. Kino, J. Myhill and R. E. Vesley, eds.,

*Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo, N.Y., 1968*, pp. 289-301. Conference on Intuitionism and Proof Theory, 1968, State University of New York at Buffalo. Studies in Logic and the Foundations of Mathematics. Amsterdam: North-Holland, 1970.

UCI Science Library QA9 C742 1968 Bar"Ordinals and Functionals in Proof Theory."

*Actes du Congrès International des Mathématiciens, 1970*, Tome 1, pp. 229-233. Publiés sous la direction du Comité d'Organisation du Congrès. 11th International Congress of Mathematicians, 1970, Nice, France. Paris: Gauthier-Villars, 1971."Infinitary Properties, Local Functors, and Systems of Ordinal Functions." In Wilfrid Hodges, ed.,

*Conference in Mathematical Logic, London '70*, pp. 63-97. Conference in Mathematical Logic, Bedford College, 1970. Lecture Notes in Mathematics, 255. Berlin & New York: Springer-Verlag, 1972."Applications of Many-Sorted Interpolation Theorems." In Leon Henkin, et al., eds.,

*Tarski Symposium, University of California, Berkeley, 1971. Proceedings*, pp. 205-223. Proceedings of Symposia in Pure Mathematics, 25. Providence: Published for the Association for Symbolic Logic by American Mathematical Society, 1974.

UCI Science Library QA7 T34 Bar"Intutionism."

*Encylopedia Brittannica*. 15th edition, pp. 633-635, 639.

Part of an article entitled "Mathematics, foundations of.""Predicatively Reducible Systems of Set Theory." In Dana S. Scott, ed.,

*Axiomatic Set Theory*, pp. 11-32 Symposium in Pure Mathematics, University of California, Los Angeles, 1967. Proceedings of Symposia in Pure Mathematics, 13, Part II. Providence: American Mathematical Society, 1971-74.

UCI Science Library QA248 S95 Bar"Two Notes on Abstract Model Theory. I. Properties Invariant on the Range of Definable Relations between Structures."

*Fundamenta Mathematicae*(1974), 82:153-165.

Collection of articles dedicated to Andrzej Mostowski on the occasion of his sixtieth birthday.

UCI Science Library QA 1 F8 Drum"Intuitonism." "Intuitonistic Foundations of Mathematics." (part of an article on "Mathematics, Foundations of)." In

*Encyclopaedia Brittanica.*15th edition. Micropaedia/Knowledge in Depth, Vol. 23, pp. 568-570, 574. Chicago: Encyclopaedia Brittanica, 1975."A Language of Axioms for Explicit Mathematics." In J. N. Crossley, ed.,

*Algebra and Logic: Papers from the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia*, pp. 87-139. Lecture Notes in Mathematics, 450. Berlin & New York: Springer-Verlag, 1975.

UCI Science Library QA3 L28 no. 450 Bar"Non-Extensional Type-Free Theories of Partial Operations and Classifications. I." In J. Diller and G. H. Müller, eds.,

*ISILC Proof Theory Symposion: Dedicated to Kurt Schütte on the Occasion of his 65th Birthday: Proceedings of the International Summer Institute and Logic Colloquium, Kiel, 1974*, pp. 73-118. ISILC Proof Theory Symposion, University of Kiel, 1974. Lecture Notes in Mathematics, 500. Berlin & New York: Springer-Verlag, 1975.

UCI Science Library QA3 L28 no. 500 Bar"Categorical Foundations and Foundations of Category Theory." In Robert E. Butts and Jaakko Hintikka, eds.,

*Logic, Foundations of Mathematics, and Computability Theory*, Vol. I, pp. 149-169. 5th International Congress of Logic, Methodology, and Philosophy of Science, 1975, University of Western Ontario. The University of Western Ontario Series in Philosophy of Science, 9. Proceedings of the Fifth International Congress of Logic, Methodology, and Philosophy of Science, London, Ontario, Canada, 1975, Part. 1. Dordrecht & Boston: D. Reidel, 1977.

UCI Science Library Q174 .I58 1975a pt.1 Bar"Generating Schemes for Partial Recursively Continuous Functionals: Summary." In

*Colloque International de Logique: Clermont-Ferrand, 18-25 Juillet 1975*, pp. 191-198. Centre National de la Recherche Scientifique. Colloques Internationaux du Centre National de la Recherche Scientifique, 249. Paris: Editions du C.N.R.S., 1977."Inductive Schemata and Recursively Continuous Functionals." In R. O. Gandy, and J. M. E. Hyland, eds.,

*Logic Colloquium 76: Proceedings of a Conference held in Oxford in July 1976*, pp. 373-392. Studies in Logic and the Foundations of Mathematics, 87. Amsterdam & New York: North-Holland/Elsevier, 1977.

UCI Science Library QA9.A1 L63 1976 Bar"Theories of Finite Type Related to Mathematical Practice." In Jon Barwise, H.J. Keisler, K. Kunen, Y.N. Moschovakis and A.S. Troelstra, eds.,

*Handbook of Mathematical Logic*, Part D, pp. 913-971. Studies in Logic and the Foundations of Mathematics, 90. Amsterdam & New York: North-Holland, 1977.

UCI Science Lib QA9 H32 Bar"Recursion Theory and Set Theory: A Marriage of Convenience." In J. E. Fenstad, R. O. Gandy, G. E. Sacks, eds.,

*Generalized Recursion Theory II: Proceedings of the 1977 Oslo Symposium*, pp. 55-98. Studies in Logic and the Foundations of Mathematics, 94. Amsterdam & New York: North-Holland/Elsevier, 1978."As progressoes transfinitas."

*O Teorema de Godel e a hipotese do continuo: antologica*, pp. 755-790. Organizada, prefaciada e traduzida por Manuel Lourenco. Lisbon: Fundacao Calouste Gulbenkian, 1979."Constructive Theories of Functions and Classes." In Maurice Boffa, Dirk van Dalen, and Kenneth McAloon, eds.,

*Logic Colloquium '78: Proceedings of the Colloquium held in Mons, August 1978*, pp. 159-224. Studies in Logic and the Foundations of Mathematics, 97. Amsterdam & New York: North-Holland/Elsevier, 1979.

UCI Science Library QA9 A1 L63 1978 Bar"Generalizing Set-Theoretical Model Theory and an Analogue Theory on Admissible Sets." In Jaakko Hintikka, Ilkka Niiniluoto, and Esa Saarinen, eds.,

*Essays on Mathematical and Philosophical Logic: Proceedings of the Fourth Scandinavian Logic Symposium and of the First Soviet-Finnish Logic Conference, Jyvaskyla, Finland, June 29-July 6, 1976*, pp. 171-195. Synthese Library, 122. Dordrecht, Holland & Boston: D. Reidel, 1979.

UCI Main Lib BC5 S28 1976"A More Perspicuous Formal System for Predicativity." In Kuno Lorenz, ed.,

*Konstruktionen versus Positionen: Beitr. zur Diskussion um d. konstruktive Wissenschaftstheorie: Paul Lorenzen zum 60. Geburtstag*, Vol. I, pp. 68-93. Berlin & New York: de Gruyter, 1979."Progressoes transfinitas ." In Manuel Lourenco, ed.,

*O Teorema de Godel e a hipotese do continuo: antologica*/ organizada, prefaciada e traduzida por Manuel Lourenco. Lisbon: Fundacao Calouste Gulbenkian, 1979."Sistemas ."

*O Teorema de Godel e a hipotese do continuo: antologica*. Organizada, prefaciada e traduzida por Manuel Lourenco. Lisbon: Fundacao Calouste Gulbenkian, 1979.(with Peter Aczel.) "Consistency of the Unrestricted Abstraction Principle using an Intensional Equivalence Operator." In J.P. Seldin and J.R. Hindley, eds.,

*To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism*, pp. 67-98. London & New York: Academic Press, 1980.

UCI Science Library QA9.2 T6 Bar(with Wilfried Buchholz, Wolfram Pohlers, and Wilfried Sieg.)

*Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies*. Lecture Notes in Mathematics, 897. Berlin & New York: Springer-Verlag, 1981.

__Includes__:

"Preface: How We Got from Here to There":1-15

(with W. Sieg.)"Iterated Inductive Definitions and Subsystems of Analysis":16-77

(with W. Sieg.) "Proof-Theoretic Equivalences between Classical and Constructive Theories for Analysis":78-142

UCI Science Library QA3 L28 no. 897 Bar"The Logic of Mathematical Discovery vs. the Logical Structure of Mathematics." In

*PSA 1978: Proceedings of the 1978 Biennial Meeting of the Philosophy of Science Association,*, Volume Two, pp. 309-327. East Lansing: Philosophy of Science Association, 1978.

UCI Science Library Q174 P58a Drum"Inductively Presented Systems and the Formalization of Metamathematics." In D. van Dalen, D. Lascar, and T.J. Smiley, eds.,

*Logic Colloquium '80: Papers Intended for the European summer Meeting of the Association for Symbolic Logic*, pp. 95-128. Logic Colloquium, 1980, Prague, Czechoslovakia. Studies in Logic and the Foundations of Mathematics, 108. Amsterdam & New York: North-Holland/Elsevier Science, 1982."Iterated Inductive Fixed-Point Theories: Application to Hancock's Conjecture." In George Metakides, ed.,

*Patras Logic Symposion: Proceedings of the Logic Symposion held at Patras, Greece, August 18-22, 1980*, pp. 171-196. Studies in Logic and the Foundations of Mathematics, 109. Amsterdam & & New York: North-Holland/Elsevier Science, 1982.

UCI Science Library QA9 A1 L65 1980 Bar"Monotone Inductive Definitions." In A.S. Troelstra and D. van Dalen, eds.,

*The L.E.J. Brouwer Centenary Symposium: Proceedings of the Conference held in Noordwijkerhout, 8-13 June 1981*, pp. 77-89. Studies in Logic and the Foundations of Mathematics, 110. Amsterdam & New York: North-Holland/Elsevier Science, 1982.

UCI Science Library QA9.56 L2 1981 Bar"Betweeen Constructive and Classical Mathematics." In

*Computation and Proof Theory: Proceedings of the Logic Colloquium held in Aachen, July 18-23, Part II*, pp. 143-162. Lecture Notes in Mathematics, 1104. Berlin & New York: Springer-Verlag, l984."Foundational Ways." In W. Jager, J. Moser, and R. Remmert<, eds.,

*Perspectives in Mathematics: Anniversary of Oberwolfach 1984*, pp. 147-158. Basel & Boston: Birkhauser Verlag, 1984.

UCI Science Library QA7 P47 1984 Bar"Gödel's Life and Work." In Solomon Feferman, J.W. Dawson, Jr., S.C. Kleene, G.H. Moore, R.M. Solovay, and Jean van Heijenoort, eds.,. Kurt Gödel's

*Collected Works. Vol. 1: Publications 1929-1936*, pp. 1-36. Oxford: Clarendon Press; New York: Oxford University Press, 1986.

UCI Science Library QA9 G5313 1986 Bar"Appendix. Proof Theory: A Personal Report." In Gaisi Takeuti's

*Proof Theory*, 2nd edition, pp. 447-485. Studies in Logic and the Foundations of Mathematics, 81. Amsterdam: North-Holland/Elsevier, 1987.

UCI Science Library QA9.54 T34 Bar(with Anita Burdman Feferman.) "Jean van Heijenoort." In Paris Logic Group, ed.,

*Logic Colloquium '85: Proceedings of the Colloquium held in Orsay, France, July 1985*, pp. 1-7. Studies in Logic and the Foundations of Mathematics, 122. Amsterdam & New York: North-Holland/Elsevier Science, 1987.

UCI Science Library QA9 A1 L63 1985 Bar"Kurt Gödel: Conviction and Caution." In S.G. Shanker, ed.,

*Gödel's Theorem in Focus*, pp. 96-114. Croom Helm Philosophers in Focus Series. London & New York: Croom Helm, 1988.- See "Kurt Gödel: Conviction and Caution." (1984)

UCI Science Library QA9.65 G63 1988 Bar"Turing in the Land of O(z)." In Rolf Herken, ed.,

*The Universal Turing Machine: A Half-Century Survey*, pp. 113-147. Oxford & New York: Oxford University Press, 1988.

UCI Science Library QA267 U55 1988 Bar"Weyl Vindicated:

*Das Kontinuum*70 Years Later." In Carlo Cellucci and Giovanni Sambin, eds.,*Temi e prospettive della logica e della filosofia della scienza contemporanee*, Vol. 1: Logica, pp. 59-93. Organizzato dalla Societa Italiana di Logica e Filosofia delle Scienze (SILFS): Cesena, 7-10 gennario 1987. Bologna: CLUEB [Cooperativa Libraria Universitaria Editrice Bologna], 1988.(with Patrick Suppes and Jon Barwise.) "Commemorative Meeting for Alfred Tarski." In Peter Duren, Richard A. Askey, and Uta C. Merzbach, eds.,

*A Century of Mathematics in America*, Part III, pp. 393-403. History of Mathematics, 3. Providence, R.I.: American Mathematical Society, 1989."Finitary Inductively Presented Logics." In R. Ferro, et al., eds.,

*Logic Colloquium '88: Proceedings of the Colloquium held in Padova, Italy, August 22-31, 1988*, pp. 191-220. Studies in Logic and the Foundations of Mathematics, 127. Amsterdam & New York: North-Holland/Elsevier Science, 1989."Polymorphic Typed Lambda-Calculi in a Type-Free Axiomatic Framework." In Wilfried Sieg, ed.,

*Logic and Computation: Proceedings of a Workshop held at Carnegie Mellon University, June 30-July 2, 1987*, pp. 101-136. Contemporary Mathematics (American Mathematical Society), 106. Providence, R.I.: American Mathematical Society, 1990.

UCI Science Library QA9.59 .W67 1987 Bar"Proofs of Termination and the '91' Function." In Vladimir Lifschitz, ed.,

*Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy*, pp. 47-63. Boston: Academic Press, 1991.

UCI Science Library Q335.5 A77 1991 Bar"Logics for Termination and Correctness of Functional Programs. II. Logics of Strength PRA." In Peter Aczel, Harold Simmons, and Stanley S. Wainer, eds.,

*Proof Theory: A Selection of Papers from the Leeds Proof Theory Programme, 1990*, pp. 195-225. Cambridge & New York: Cambridge University Press, 1992."Logics for Termination and Correctness of Functional Programs." In Y.N. Moschovakis, ed.,

*Logic from Computer Science: Proceedings of a Workshop held November 13-17, 1989*, pp. 195-225. Mathematical Sciences Research Institute Publications, 21. New York: Springer-Verlag, 1992.

UCI Science Library QA9 A1 L64 1992 Bar"A New Approach to Abstract Data Types. II. Computation on ADTs as Ordinary Computation." In E. Börger, G. Jäger, H. Kleine Büning and M.M. Richter, eds.,

*Computer Science Logic: 5th Workshop, CSL '91, Berne, Switzerland, October 1991: Proceedings*, pp. 79-95. Lecture Notes in Computer Science, 626. Berlin & New York: Springer-Verlag, 1992.

UCI Science Library QA75.5 W624 1991 Bar"Turing's 'Oracle': From Absolute to Relative Computability--and Back." In Javier Echeverria, Andoni Ibarra, and Thomas Mormann, eds.,

*The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations*, pp. 314-348. Foundations of Communication and Cognition. Berlin & New York: de Gruyter, 1992."Appendix. Jean van Heijenoort's Scholarly Work." In Anita Burdman Feferman's

*Politics, Logic, and Love: The Life of Jean Van Heijenoort*, pp. 371-390. Boston: Jones and Bartlett; Wellesley, Mass.: A. K. Peters, 1993.

UCI Main Library B2430 V36 F44 1993"Gödel's

*Dialectica*Interpretation and Its Two-Way Stretch." In Georg Gottlob, Alexander Leitsch and Daniele Mundici, eds.*Computational Logic and Proof Theory: Third Kurt Gödel Colloquium, KGC'93, Brno, Czech Republic, August 1993: Proceedings*, pp. 23-40. Lecture Notes in Computer Science, 713. Berlin & New York: Springer-Verlag, 1993.

UCI Science Library QA76.9 A96 K87 1993 Bar"What Rests on What? The Proof-Theoretic Analysis of Mathematics." In Johannes Czermak, ed.,

*Philosophy of Mathematics: Proceedings of the 15th International Wittgenstein-Symposium: 16th to 23rd August 1992, Kirchberg am Wechsel(Austria)/Philosophie der Mathematik: Akten des 15. Internationalen Wittgenstein-Symposiums: 16. bis 23. August 1992, Kirchberg am Wechsel (Osterreich)*, Vol. 1, pp. 147-171. Schriftenreihe der Wittgenstein-Gesellschaft, 20. Vienna: Hölder-Pichler-Tempsky, 1993.

UCI Main Library B3376 W564 A17 Bd.20"Why a Little Bit Goes a Long Way: Logical Foundations of Scientifically Applicable Mathematics."

*PSA: Proceedings of the 1992 Biennial Meeting of the Philosophy of Science Association*(1993), 2:442-455.

UCI Science Library Q174 P58a Drum"Working Foundations--'91." In Giovanna Corsi, Maria Luisa Dalla Chiara, and Gian Carlo Ghirardi, eds.,

*Bridging the Gap: Philosophy, Mathematics, and Physics: Lectures on the Foundations of Science*, pp. 99-124.*Boston Studies in the Philosophy of Science*, 140. Dordrecht & Boston: Kluwer Academic, 1993.

UCI Science Library Q174 B67 v.140 Bar"Finitary Inductively Presented Logics." In D.M. Gabbay, ed.,

*What Is a Logical System?*pp. 297-328. Studies in Logic and Computation, 4. Oxford Science Publications. Oxford: Clarendon Press; New York: Oxford University Press, 1994.(with Sergei Artemov, George Boolos, Erwin Engeler, Gerhard Jäger, and Albert Visser.) "Preface."

*Annals of Pure and Applied Logic*(September 12, 1995), 75(1-2):1.- Issue is entitled "Invited papers presented at the Conference on Proof Theory, Provability Logic, and Computation, March 20-24, 1994, Berne, Switzerland."

UCI Science Library BC135 A4 Drum"Ordinal Logic." In Robert Audi, ed.,

*The Cambridge Dictionary of Philosophy*, pp. 550-551. Cambridge: Cambridge University Press, 1995.

UCI Main Library Reference B41 C35 1995"Ordinal Logics." In Edward Craig, ed.,

*The Routledge Encyclopedia of Philosophy*, Vol. 7, pp. 139-143. London & New York: Routledge, 1998.

UCI Main Library Reference B51 R68 1998"Reflection Principles." In Robert Audi, ed.,

*The Cambridge Dictionary of Philosophy*, p. 682. Cambridge: Cambridge University Press, 1995.

UCI Main Library Reference B41 C35 1995"Gödel's Program for New Axioms: Why, Where, How and What?" In Petr Hajek, ed.,

*Godel '96: Logical Foundations of Mathematics, Computer Science, and Physics--Kurt Godel's Legacy: Brno, Czech Republic, August 1996, Proceedings*, pp. 3-22. Lecture Notes in Logic, 6. Berlin & New York: Springer, 1996.

UCI Science Library QA9 A1 G6 1996 Bar"Kreisel's 'Unwinding' Program." In Piergiorgio Odifreddi, ed.,

*Kreiseliana: About and Around Georg Kreisel*, pp. 247-273. Wellesley, Mass.: A.K. Peters, 1996."Proof Theory." In Donald M. Borchert, ed.,

*The Encyclopedia of Philosophy. Supplement*, pp.466-469. New York: Macmillan Reference USA, Simon & Schuster Macmillan; London: Simon & Schuster and Prentice Hall International, 1996.

UCI Main Lib B41 E5 1996 Reference(with Jeremy Avigad.) "Gödel's Functional ('Dialectica') Interpretation." In Samuel R. Buss, ed.,

*Handbook of Proof Theory*, pp. 337-405. Studies in Logic and Foundations of Mathematics, 137. New York: Elsevier, 1998.

UCI Science Library QA9.54 H35 1998 Bar(with Geoffrey Hellman.) "Challenges to Predicative Foundations of Arithmetic." In Gila Sher and Richard L. Tieszen, eds.,

*Between Logic and Intuition: Essays in Honor of Charles Parsons*, pp. 317-339. Dordrecht & Boston: Kluwer Academic, 1999."Tarski and Gödel: Between the Lines." In Jan Wolenski and Eckehart Kohler, eds.,

*Alfred Tarski and the Vienna Circle: Austro-Polish Connections in Logical Empiricism*, pp. 53-63. Vienna Circle Institute Yearbook, 6. Dordrecht & Boston: Kluwer, 1999."Ah, Chu." In

*JFAK: Essays Dedicated to Johan van Benthem on the Occasion of his Fiftieth Birthday*. Amsterdam University Press. CD-ROM.- See "Kurt Gödel: Conviction and Caution." (1984)

(with R.L. Vaught.) "The First Order Properties of Products of Algebraic Systems."

*Fundamenta Mathematica*(1959), 47:57-103.

UCI Science Library QA1 F8 Drum(with A. Ahrenfeucht.) "Representability of Recursively Enumerable Sets in Formal Theories."

*Archiv für Mathematische Logik und Grundlagenforschung*(1959), 5:37-41."Arithmetization of Metamathematics in a General Setting."

*Fundamenta Mathematica*(1960), 49:35-92.(with G. Kreisel and S. Orey.) "l-Consistency and Faithful Interpretations."

*Archiv für Mathematische Logik und Grundlagenforschung*(1960), 5:52-63."Classifications of Recursive Functions by Means of Hierarchies."

*Transactions of the American Mathematical Society*(July 1962), 104:101-122.

UCI Science Library QA1 A522 Drum(with C. Spector.) "Incompleteness Along Paths in Progressions of Theories."

*Journal of Symbolic Logic*(December 1962), 27(4):383-390.

UCI Science Library BC1 J6 Drum"Transfinite Recursive Progressions of Axiomatic Theories."

*Journal of Symbolic Logic*(September 1962), 27(3):259-316.

UCI Science Library BC1 J6 Drum"Systems of Predicative Analysis."

*Journal of Symbolic Logic*(March 1964), 29(1):1-30.

UCI Science Library BC1 J6 Drum"Some Applications of the Notions of Forcing and Generic Sets."

*Fundamenta Mathematicae*(1965), 56:325-345.

UCI Science Library QA1 F8 Drum(with G. Kreisel.) "Persistent and Invariant Formulas Relative to Theories of Higher Order."

*Bulletin of the American Mathematical Society*(May 1966), 72(3) [702]:480-485.

UCI Science Library QA1 A52 Drum"Predicative Provability in Set Theory."

*Bulletin of the American Mathematical Society*May (1966), 72(3) [702]:486-489.

UCI Science Library QA1 A52 Drum"Persistent and Invariant Formulas for Outer Extensions."

*Compositio Mathematica*(1968), 20:29-52.

The issue is dedicated to A. Heyting on the occasion of his 70th birthday.

UCI Science Library QA1 C73 Drum"Systems of Predicative Analysis, II: Representation of Ordinals."

*Journal of Symbolic Logic*(June 1968), 33(2):193-220.

UCI Science Library BC1 J6 Drum"Two Notes on Abstract Model Theory. I. Properties Invariant on the Range of Definable Relations between Structures."

*Fundamenta Mathematicae*(1974), 82:153-165.

Collection of articles dedicated to Andrzej Mostowski on the occasion of his sixtieth birthday.

UCI Science Library QA 1 F8 Drum"Two Notes on Abstract Model Theory. II. Languages for which the Set of Valid Sentences is Semi-Invariantly Implicitly Definable."

*Fundamenta Mathematicae*(1975), 89(2):111-130."Recursion in Total Functionals of Finite Type."

*Compositio Mathematica*(1977), 35(1):3-22.

UCI Science Lib QA1 C73 Bar(with Jon Barwise and Leo Harrington.) "Reno, 1976."

*Journal of Symbolic Logic*(March 1977), 42(1):156.

UCI Science Library BC1 J6 Drum"What Does Logic have to Tell Us about Mathematical Proofs?"

*Mathematical Intelligencer*(1979-80), 2(1):20-24.

UCI Science Library QA1 M427 Drum(with G. Jäger.) "Choice Principles, the Bar Rule and Autonomously Iterated Comprehension Schemes in Analysis."

*Journal of Symbolic Logic*(March 1983), 48(1):63-70.

UCI Science Library BC1 J6 Drum"Kurt Gödel: Conviction and Caution."

*Philosophia Naturalis*(1984), 21(2-4):546-562.

This issue is on "Philosophy of Science/History of Science."

UCI Main Library B3 P62"Toward Useful Type-Free Theories."

*Journal of Symbolic Logic*(March 1984), 49(1):75-111.

This issue includes: "A Selection of Contributed Papers of the 7th International Congress of Logic, Methodology and Philosophy of Science, Salzburg, 1983." Edited by Paul Weingartner and Christine Pühringer."Intensionality in Mathematics."

*Journal of Philosophical Logic*(February 1985), 14(1):41-55.

UCI Main Library BC51 J68"A Theory of Variable Types."

*Revista Colombiana de Matématicas*(1985), 19(1-2):95-105.

Part of the Proceedings of the 5th Latin American Symposium on Mathematical Logic, Bogotá, 1981."Working Foundations."

*Synthese*(February 1985), 62(2):229-254.

This issue contains papers given at the Conference on "The Present State of the Problem of Foundations of Mathematics, Florence, 1981."

UCI Science Library Q4 S9 Drum"Hilbert's Program Relativized: Proof-Theoretical and Foundational Reductions."

*Journal of Symbolic Logic*(June 1988), 53(2):364-384.

UCI Science Library BC1 J6 Drum"Infinity in Mathematics: Is Cantor Necessary?"

*Philosophical Topics*(Fall 1989), 17(2):23-45.

This issue is entitled "Philosophy of Mathematics."

UCI Main Library B1 S58"Reflecting on Incompleteness."

*Journal of Symbolic Logic*(March 1991), 56(1):1-49.

Retiring Presidential Address.

UCI Science Library BC1 J6 Drum(with Anita Burdman Feferman.) "Jean van Heijenoort (1912-1986)."

*Modern Logic*(1992), 2(3):231-238."A New Approach to Abstract Data Types. I. Informal Development."

*Mathematical Structures in Computer Science*(1992), 2(2):193-229.(with Gerhard Jäger.) "Systems of Explicit Mathematics with Non-Constructive Mu-Operator." (Part I)

*Annals of Pure and Applied Logic*(December 15, 1993), 65(3):243-263.

UCI Science Library BC135 A4 Drum"Julia Bowman Robinson, December 8, 1919 - July 30, 1985."

*Biographical Memoirs of the National Academy of Sciences*(1994), 63:453-478."Definedness."

*Erkenntnis*(November 1995), 43(3):295-320.

Presented at a mini-Conference on 17 February 1995 at the University of California at Irvine, under the auspices of the UCI Program in the History and Philosophy of Science.

Issue is entitled: "Varia, with a Workshop on the Foundations of Partial Functions and Programming (Irvine, CA, 1995)." Edited by Karel Lambert.

UCI Main Library B1 J79(with Sergei Artemov, George Boolos, Erwin Engeler, Gerhard Jäger, and Albert Visser.) "Preface."

*Annals of Pure and Applied Logic*(September 12, 1995), 75(1-2):1.

Issue is entitled "Invited papers presented at the Conference on Proof Theory, Provability Logic, and Computation, March 20-24, 1994, Berne, Switzerland."

UCI Science Library BC135 A4 Drum(with Geoffrey Hellman.) "Predicative Foundations of Arithmetic."

*Journal of Philosophical Logic*(February 1995), 24(1):1-17.

UCI Main Library BC51 J68"Computation on Abstract Data Types: The Extensional Approach, with an Application to Streams."

*Annals of Pure and Applied Logic*(September 1996), 81(1-3):75-113.

Dedicated to the late Stephen Cole Kleene.

UCI Science Library BC135 A4 Drum"Penrose's Gödelian Argument."

*Psyche*(1996), 2:21-32.(with Gerhard Jäger.) "Systems of Explicit Mathematics with Non-Constructive Mu-Operator." (Part II)

*Annals of Pure and Applied Logic*(May 2, 1996), 79(1):37-52.

UCI Science Library BC135 A4 Drum"My Route to Arithmetization."

*Theoria*(1997), 63:168-181.

UCI Main Library Current Periodical Room B1 A27"Does Mathematics Need New Axioms?"

*American Mathematical Monthly*(February 1999), 106(2):99-111.

UCI Science Library QA1 A515"Logic, Logics, and Logicism."

*Notre Dame Journal of Formal Logic*. (Forthcoming)"Mathematical Intuition vs. Mathematical Monsters."

*Synthese*(Forthcoming).(with T. Strahm.) "The Unfolding of Non-Finist Arithemtic."

*Annals of Pure and Applied Logic*. (Forthcoming)

Review of Gaisi Takeuti's

*Proof Theory*.*Bulletin of the American Mathematical Society*(May 1977), 83(3) [768]:351-361.

UCI Science Library QA 1 A5202 DrumReview of Kurt Schütte's

*Proof Theory*(Translated by J.N. Crossley).*Bulletin of the American Mathematical Society*(New Series) (1979), 1:224-228.

UCI Science Library QA1 A5202 DrumReview of Ray Mines and Fred Richman's

*A Course in Constructive Algebra*.*American Scientist*(July-August 1989), 77(4):402.

UCI Science Library Q11 A47 Drum

"Product Operations on Relational Systems." [Abstract]

*Bulletin of the American Mathematical Society*(March 1955), 61:172.

UCI Science Library QA1 A5202 Drum"Sum Operations on Relational Systems." [Abstract]

*Bulletin of the American Mathematical Society*(March 1955), 61:172.

UCI Science Library QA1 A5202 Drum"Degrees of Unsolvability Correlated to Theories with Standard Formalization." [Abstract]

*Bulletin of the American Mathematical Society*(July 1956), 2:412.

UCI Science Library QA1 A5202 Drum(with R.L. Vaught.) "Elimination of Quantifiers in the Theory of Generalized Products." [Abstract]

*Bulletin of the American Mathematical Society*(July 1957), 63:290. UCI Science Library QA1 A5202 Drum"Formal Consistency Proofs and Interpretability of Theories." [Abstract]

*Journal of Symbolic Logic*(March 1957), 22(1):107.

UCI Science Library BC1 J6 Drum(with R.L. Vaught.) "Model-Theoretic and Decidability Theorems Concerning Generalized Products." [Abstract]

*Bulletin of the American Mathematical Society*(July 1957), 63:289.

UCI Science Library Drum"Sentences of Arithmetic which Formally Express Consistency." [Abstract]

*Journal of Symbolic Logic*(March 1957), 22(1):106-107.

UCI Science Library BC1 J6 Drum"Ordinal Logics Re-Examined." [Abstract]

*Journal of Symbolic Logic*(March 1958), 23(1):105.

UCI Science Library BC1 J6 Drum"On the Strength of Ordinal Logics." [Abstract]

*Journal of Symbolic Logic*(March 1958), 23(1):105-106.

UCI Science Library BC1 J6 Drum"Some Completeness Results for Recursive Progressions of Theories. (Ordinal Logics)." [Abstract]

*Journal of Symbolic Logic*(1959), 24:312-313.

UCI Science Library BC1 J6 Drum

"Formal Consistency Proofs and Interpretability of Theories." Ph.D. Dissertation in Mathematics, University of California, Berkeley, 1957.

Avigard, Jeremy. Review of Solomon Feferman's

*In the Light of Logic*(1998).*Journal of Philosophy*(December 1999), 96(2):638-642.Sandu, Gabriel. "If-Logic and Truth-Definition."

*Journal of Philosophical Logic*(April 1998), 27(2):143-164.

UCI Main Library BC51 J68Turner, Raymond. "Three Theories of Nominalized Predicates."

*Studia Logica*(1985), 44:165-186. UCI Main Library B18 P6 S88- Vourtsanis, Yiannis.
"A Direct Proof of the Feferman-Vaught Theorem and Other
Preservation
Theorems in Prodycts."
*Journal of Symbolic Logic*(June 1991), 56(2):632-636. Weiermann, Andreas. "A Functorial Property of the Aczel-Buchholz-Feferman Function."

*Journal of Symbolic Logic*(September 1994), 59(3):945-955.

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