Bibliography of Georg Kreisel, F .R.S. . I Chronological Listing of Research Papers, Essays, Lecture Notes, and Technical Reports1

Version of L{ August 1990

1. Kreisel, G. Some remarl..:s on integral equations with kernels: L(6 - x 1 , .. . , ~n - Xni a). Proceedings of the Royal Society ,A, vol. 197 (1949), pp. 160-183.

2. Kreisel, G. Surface wa·ves. Quarterly of Applied , vol. 7 (1949), pp. 21-44.

3. Kreisel, G. Note on arithmetic models for consistent formulae of the predicate calculus. Fundamenta Mathematicae, vol. 37 (1950), pp. 265-285.

4. Kreisel, G. On the interp1·etation of non-finitist proofs I. The Journal of Symbolic Logic, vol. 16 (1951), pp. 241-267.

5. Kreisel, G. Some remar!.s on the foundation of ma.thematics. An expository article. The Mathematical Gazette, vol. 35 (1951), pp. 23-28.

6. Kreisel, G. On the concepts of completeness and interpretation of formal systems. Fundamenta Mathematicae, vol. 39 (1952), pp. 103-127.

7. Kreisel, G. Some elementanJ inequalities. Indagationes Mathematicae, vol. 14 (1952), pp. 334-338.

8. Kreisel, G. On the intfrpretation of non-finitist ptoofs II. lnterpretatiqn of number theory. Applications. The Journal of Symbolic I,ogic, vol. 17 (1952), pp. 43-58.

9. Kreisel, G. Some concepts concerning formal systems of number theory. . Mathema­ tische Zeitschrift, vol. 57 (1952), pp. 1-12.

10. Kreisel, G. Note on arithmetic models for consistent formulae of the predicate. calculus II. in: Actes du XIeme Congres International de Philosophie, Bruxelles, 20-26 A011t 1953, Volu1ne 14. North-Holland Publishing Company, 1953, pp. 39- 49.

11. Kreisel, G. A variant to Hilbert's theory of the foundations of arithmetic. British Journal for the Philosophy of Science, vol. 4 (1953), pp. 107-129, 357.

12. Kreisel, G. Review of "The diagonal method .in forma"lized arithmetic". British Jour­ nal for the Philosophy of Science, vol. 3 (1953), pp. 364-374.

1 Reviews from the Journal of Symbolic Logic and the Zentralblatt fiir Mathematik are not included in this listing, but other e:;say" reviews are.

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13. Kreisel, G. On a problem. of Henkin's. Indagationes Mathematicae, vol. 15 (1953), pp. 405-406.

14. Kreisel, G. Note on functional relationship. Mathematical Gazette, vol. 37 (1953), pp. 18-20.

15. Kreisel, G. Applications of to various branches of mathematics. in: Applications Scientifiques de la Logique. Mathematique. Actes du 2e Colloque International de Logique Mathematique, Paris-25-30 aout 1952, Inst!tut Henri Poincare, edited by J.-1. Destouches and P. Destouches-Fevrier. Gauthier-Villars Editeur, 1954, pp. 37- 49. 16. Kreisel, G. Discussion sur divers themes. in: Applications Scientifiques de la Logique Mathematique. Actes du 2e Colloque International de Logique Mathematique, Paris- 25-30 aout 1952, Institut Henri Poincare, edited by J.-1. Destouches and P. Destouches-Fevrier. Gauthier-Villars Editeur, 1954, pp. 157- 158. 17. Kreisel, G. Remark on complete interpretations by models. Archiv fiir Mathema­ tische Logik und Gru~dlagenforschung, vol. 2 (1954), pp. 4- 9. 18. Kreisel, G. Remark on complete interpretations by models. Archiv fiir Philosophie, vol. 5 (1954), pp. 84- 89. 19. Kreisel, G. Bases for systems of analysis. in: Proceedings of the International Congress of Mathematicians 1954, edited by J. Gerretsen and J . de Groot. vol. 2, North-Holland Publishing Company, 1954, p. 405.

20. Kreisel, G. and Wang, IL Some applications of formalized consistency proofs. Fun­ damenta Mathematicae, vol. 42 (1955), pp. 101- 110.

21. Kreisel, G. Models, trans!ations and interpretations. in: Mathematical Interpreta­ tion of Formal Systems, edited by T. Skolem. North-Holland Publishing Company, 1955, pp. 26- 50.

22. Kreisel, G. Review of "Some uses of metamathematics". British Journal for the Philosophy of Science; vol. 7 (1956), pp. 161- 173.

23. Kreisel, G., Lacombe, D., and Shoenfield, J . Fonctionnelles recursivement definissables et fonctionnelles recursives. Academie des Sciences de Paris. Comptes Rendus Hebdomadaires des Seances, vol. 245 (1957), pp. 399-402.

24. Kreisel, G. and Lacombe, D. Ensembles recursivement mesurables et ensembles recursivement ouverts ou fermes. Academie des Sciences de Paris. Comptes Rendus Hebdomadaires des Seances, vol. 245 (1957), pp. 1106- 1109.

25. Kreisel, G. and Putnam, H. Eine Unableitbarkeitsbeweismethode fiir den intuition­ istischen Aussagenkalkiil. Archiv fiir Mathematische Logik und Grundlagen­ forschung, vol. 3 (1957), pp. 74-78.

2 26. Kreisel, G. Independent recursive axiomatization. The Journal of Symbolic Logic, vol. 22 (1957), p. 109. [Abstract].

27. Kreisel, G. Godel's interpretation of Heyting's arithmetic. in: Summaries of Talks Presented at the Summer Institute for Symbolic Logic Cornell University 1957, edited by J. Rosser. Department of Mathematics, Cornell University, 1957, pp. 125-133A. [Reprinted 1960].

28. Kreisel, G. Relations between classes of constructiv~ functionals. in: Summaries of Talks Presented at the Summer Institute or' Symbolic Logic Cornell Uni­ versity 1957, edited by J. Rosser. Department of Mathematics, Cornell University, 1957, pp. 292-302. [Reprinted 1960].

29. Kreisel, G. Sums of squares. in: Summaries of Talks Presented at the Summer Institute for Symbolic Logic Cornell University 1957, edited by J. Rosser. Department of Mathematics, Cornell University, 1957, pp. 313-320. [Reprinted 1960].

30. Kreisel, G., Lacombe, D., and Shoenfield, J. Effective operations and partial recursive functionals. in: Summaries of Talks Presented at the Summer Institute for Symbolic Logic Cornell University 1957, edited by J. Rosser. Department of Mathematics, Cornell University, 1957, pp. 364-365. (Reprinted 1960].

31. Kreisel, G. Review of "Wittgenstein's remarks on the foundations of mathematics". British Journal for the Philosophy of Science, vol. 9 (1958), pp. 135-158.

32. Kreisel, G. Hilbert's programme. Dialectica. International Review of Philosophy of Knowledge, vol. 12 (1958), pp. 346-372.

33. Kreisel, G. Hilbert's programme. in: Logica: Studia Paul Bernays Dedicata. Editions du Griffon, 1958, pp. 142-168. [Reprint of Dialectica paper].

34. Kreisel, G. and Wang, H,. Applications of formalized consistency proofs II. Funda­ menta Mathematicae, vol. 45 (1958), pp. 334- 335.

35. Kreisel, G. Mathematical significance of consistency proofs. The Journal of Sym­ bolic Logic, vol. 23 (1958), pp. 155-182.

36. Kreisel, G. Elementary completeness properties of .intuitionistic logic with a note on negations of prenex formulae. The Journal of Symbolic Logic, vol. 23 (1958), pp. 317-330.

37. Kreisel, G. A remark on free choice sequences and the topological completeness proofs. The Journal of Symbolic Logic, vol. 23 (1958), ·PP· 369-388.

38. Kreisel, G. Principles of Constructive Mathematics. Lectures delivered at Stan­ ford University, 1958-1959, 80 lectures, unnumbered pp. [Mimeographed].

3 39. Kreisel, G., Shoenfield, J., and Wang, H. Number theoretic concepts and recursive well-orderings. Archiv fiir Mathematische Logik und Grundlagenforschung, vol. 5 (1959), pp. 42-64.

40. Kreisel, G. Analysis of the Cantor-Bendixson theorem by means of the analytic hi­ erarchy. Bulletin de l' Academie Polonaise des Sciences. Serie des Sciences Mathematiques, Astronomiques et Physiques, vol. 7 (1959), pp. 621-626.

41. Kreisel, G. Interpretation of analysis by means of constructive functionals of finite types. in: Constructivity in Mathematics, edited by A. Heyting. North-Holland Publishing Company, 1959, pp. 101-128.

42. Kreisel, G., Lacombe, D., and Shoenfield, J. Partial recursive functionals and effective operations. in: Constructivity in Mathematics, edited by A. Heyting. North­ Holland Publishing Company, 1959, pp. 290-297. I 43. Kreisel, G. Proof by transfinite induction and definition by transfinite recursion in quantifier free systems. The Journal of Symbolic Logic, vol. 24 (1959), pp. 322- 323. [Abstract].

44. Kreisel, G. Review of "Wittgenstein's theory and practice of philosophy". British Journal for the Philosophy of Science, vol. 11 (1960), pp. 238-252.

I 45. Kreisel, G. Non-uniqueness results for transfinite progressions. Bulletin de l'Academie Polonaise des Sciences. Serie des Sciences Mathematiques, As­ tronomiques et Physiques, vol. 8 (1960), pp. 287-290.

46. Gandy, R., Kreisel, G., and Tait, W. Set existence. Bulletin de l'Academie Polon­ aise des Sciences. Serie des Sciences Mathematiques, Astronomiques et Physiques, vol. 8 (1960), pp. 577-582.

47. Kreisel, G. La predicatiVite. Bulletin de la Societe Mathematique de France, vol. 88 (1960), pp. 371-391.

I 48. Kreisel, G. The status of the first e-number in first order arithmetic. The Journal of Symbolic Logic, vol ~ 25 (1960), p. 390. [Abstr~.ct].

49. Kreisel, G. Ordinals of ramified analysis. The Journal of Symbolic Logic, vol. 25 (1960), pp. 390- 391. [Abstract].

50. Kreisel, G. Ordinal logics and the characterization of informal concepts of proof in: Proceedings of the International Congress of Mathematicians: 14-21 Au­ gust, 1958, edited by J. Todd. The Cambridge University Press, 1960, pp. 289-299.

51. Huber-Dyson, V. and Kreisel, G. Analysis of Be.th's semantic construction of intuitionistic logic. Applied Mathematics and Statistic Laboratories, Stanford Uni­ versity, 1961, 65 pp. [Technical Report].

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52. Gandy, R., Kreisel, G., and Tait, W. Set existence II. Bulletin de l'Academie Polonaise des Sciences. Serie des Sciences Mathematiques, Astronomiques et_Physiques, vol. 9 (1961), pp. 881- 882.

53. Kreisel, G. Set theoretic problems suggested by the notion of potential totality. in: In­ finitistic Methods. Proceedings of the Symposium on Foundations of Math­ ematics. Panstwowe Wydawnictwo Naukowe (PWN), 1961, pp. 103-140.

54. Kreisel, G. Note on completeness and definability. Applied Mathematics and Statistic Laboratories, Stanford University, 1961, 38 pp. [Technical Report].

55. Kreisel, G. On weak completeness of intuitionistic predicate logic. Applied Mathematics and Statistics Laboratories, Stanford University, 1961, 38 pp. [Technical Report].

56. Kreisel, G. and Tait, W. Finite definability of nu~ber-theoretic functions and para­ metric completeness of equational calculi. Zeitschrift fiir Mathematische Logik und Grundlagen der Mathematik, vol. 7 (1961), pp. 28-38.

57. Kreisel, G. Intuitionistic Mathematics. Lecture delivered at Stanford University, 1962?, 270 pp. [Mimeographed].

58. Feferman, S., Kreisel, G., and Orey, L. 1-consistency and faithful interpretations. Archiv fiir Mathematische Logik und Grundlagenforschung, vol. 6 (1962), pp. 52-63.

59. Kreisel, G. The axiom of choice and the class of h'!J·perarithmetic functions. Indaga­ tiones Mathematicae, vol. 24 (1962), pp. 307-319.

60. Kreisel, G. On weak completeness of intuitionistic predicate logic. The Journal of Symbolic Logic, vol. 27 (1962), pp. 139-158.

61. Kreisel, G. Proof theoretic results on intuitionisticfirst order arithmetic. The Journal of Symbolic Logic, vol. 27 (1962), pp. 379-380. [Abstract].

62. Kreisel, G. Proof theoretic results on intuitionistic higher order arithmetic. The Journal of Symbolic I;ogic, vol. 27 (1962), p. 380. [Abstract].

63. Kreisel, G. Consequences of Brouwer 's bar theorem. The Journal of Symbolic Logic, vol. 27 (1962), pp. 380-381. [Abstract].

64. Kreisel, G. Foundations ~f intuitionistic logic. in: Logic, Methodology and Philos­ ophy of Science, edited by .E. Nagel, P. Suppes, and A. Tarski. Stanford University Press, 1962, pp. 198-210.;

65. Kreisel, G. Review of "Beweistheorie". The Mathematical Gazette, vol. 46 (1962), pp. 250-255.

5 66. Kreisel, G. Reports of the Seminar on Foundations of Analysis. Stanford University, 1963, 171 pp. [Technical report collection, mimeographed].

67. Kreisel, G. Hilbert's programme. in: Philosophy of Mathematics. Selected Read­ ings, edited by P. Benacerraf and H. Putnam. Prentice Hall, 1964, pp. 157-180. [Revised reprint].

68. Kreisel, G. and Sacks, G. Metarecursive sets. The Journal of Symbolic Logic, vol. 30 (1965), pp. 318-338.

69. Kreisel, G. Mathematical. Logic. in: Lectures on IVIodern Mathematics, edited by T. Saaty. vol. 3, J. Wiley & Sons, 1965, pp. 95-195.

70. Kreisel, G. Mathematical Logic. in: Lectures on Modern Mathematics, edited by T. Saaty. Iwanami Shoten, 1965, pp. 128-291. [Japanese translation].

71. Kreisel, G. Model-theoretic invariants: Applications to recursive and hyperarithmetic operations. in: The Theory of Models, edited by J. Addison, L. Henkin, and A. Tarski. North-Holland Publishing Company, 1965, pp. 190-205.

72. Ehrenfeucht, A. and Kreisel, G. Strong models of arithmetic. Bulletin de l'A­ cademie Polonaise des Sciences. Serie des Sciences Mathematiques, As­ tronomiques et Physiques, vol. 14 (1966), pp. 107-110.

73. Feferman, S. and Kreisel, G. Persistent and invaria,nt formulas relative to theories of higher order. Bulletin of the American Mathe1matical Society, vol. 72 (1966), pp. 480-485.

74. Howard, W. and Kreisel, G. Transfinite induction and bar induction of types zero and one, and the role of continuity in intuitionistic analysis. The Journal of Symbolic Logic, vol. 31 (1966), pp. 325-358.

75. Kreisel, G. Review of "Survey of Mathematical Logic". The Philosophical Review, vol. 75 (1966), pp. 240-244.

76. Kreisel, G. Mathematical logic: What has it done for the philosophy of mathematics'? in: : Philosopher of the Century. Essays in his Honour, edited by R. Schoenmann. George Allen & Un.win, 1967, pp. 201-272. (Addenda on pp. 315-316].

77. Kreisel, G. and Krivine, J.-L. Elements de Logique Mathematique: Theorie des Modeles. Dunod, 1967, viii+213 pp.

78. Kreisel, G. and Krivine, J.-L. Elements of Mathematical Logic (Model Theory). North-Holland Publishing Company, 1967, xi+222 pp. [First English edition].

79. Kreisel, G. Relative recursiveness in metarecursion theory. The Journal of Sym­ bolic Logic, vol. 32 (1967), p. 442. [Abstract].

6 80. Kreisel, G. Relative recursive enumerability in metarecursion theory. The Journal of Symbolic Logic, vol. 32 (1967), pp. 442-443. [Abstract].

81. Kreisel, G. Informal rigour and completeness proofs. in: Problems in the Philos­ ophy of Mathematics. Proceedings of the International Colloquium in the Philosophy of Science, Volume 1, edited by I. Lakatos. North-Holland Publishing Company, 1967, pp. 138-186. ' 82. Kreisel, G. Lawless sequences of natural numbers. Compositio Mathematica, vol. 20 (1968), pp. 222-248.

83. Kreisel, G. Elements of . Lectures delivered at University of Califor­ nia, Los Angeles, 1968, 165 pp. [Mimeographed).

84. Kreisel, G. A survey of proof theory. The Journal of Symbolic Logic, vol. 33 (1968), pp. 321-388.

85. Kreisel, G. The role of co in finite extensions of elementary analysis, Z1 • Journal of Symbolic Logic, vol. 33 (1968), p. 492. [Abstract).

86. Kreisel, G. So-called consistency proofs by means of transfinite induction: Provable ordinals. Journal of Symbolic Logic, vol. 33 (1968), p. 493. [Abstract).

87. Kreisel, G. Functions, ordinals, species. in: Logic, Methodology and Philosophy of Science III. Proceedings of the Third International Congress, Amster­ dam, 1967, edited by B. van Root.selaar and J. Staal. North-Holland Publishing I Company, 1968, pp. 145-159.

88. Kreisel, G. Foundations of Mathematics: 1900-1950. in: Scientific Thought 1900- 1960, edited by R. Harre. Oxford University Press, 1968, pp. 4-13.

89. Kreisel, G. Choice of infi;'titary languages by means pf definability criteria; generalized recursion theory. in: The Syntax and Semantics of Infinitary Languages, edited by J. Barwise. Lecture Notes in Computer Science, vol. 72, Springer-Verlag, 1968, pp. 139-151.

90. Kreisel, G. and Levy, A. Reflection principles and their use for establishing the com­ plexity of axiomatic systems. Zeitschrift fiir Mathematische Logik und Grund­ lagen der Mathematik, vol. 14 (1968), pp. 97-142.

91. Kreisel, G. Algebraic Proof Theory. Lecture Notes delivered at Stanford Univer­ sity, 1969, 66 pp. [Mimeographed].

92. Kreisel, G. Axiomatizations of nonstandard analysis that are conservative extensions of formal systems for classical standard analysis. in: Applications of Model Theory to Algebra, Analysis and Probability, edited by W. Luxemburg. Holt Rinehart & Winston, 1969, pp. 93--106.

7 93. Kreisel, G. and M.A.H. Newman. Luitzen Egbertus Jan Brouwer {1881-1966}. Bio­ graphical Memoirs of Fellows of the Royal Society, vol. 15 (1969), pp. 39-68.

94. Kreisel, G. Two notes on the foundations of . Dialectica. International Review of Philosophy of Knowledge, vol. 23 (1969), pp. 93-114.

95. Kreisel, G. Informal rigour and completeness proofs. in: The Philosophy of Math­ ematics, edited by J. Hintikka. Oxford University Press, 1969, pp. 78-94. [Reprint with a postscript].

96. Kreisel, G. Mathematical Logic: What has it done for the philosophy of mathematics? in: The Philosophy of Mathematics, edited by J. Hintikka. Oxford University Press, 1969, pp. 147-152. [Reprint].

97. Kreisel, G. Appendix II. Category theory and the foundations of mathematics. in: Reports of the Midwest Category Seminar HI, edited by M. Barr. vol. 106, Springer-Verlag, Lecture Notes in Mathematics, 1969, pp. 233-247.

98. Kreisel, G. and Troelstra, A. Formal systems for some branches of intuitionistic anal­ ysis. Annals of Mathematical Logic, vol. 1 (1970), pp. 229-387.

99. Kreisel, G. Church's thesis: A kind of reducibility axiom for constructive mathematics. in: Intuitionism and Proof Theory, edited by A. Kino, J. Myhill, and R. Vesley. North-Holland Publishing Company, 1970, pp. 121-150.

100. Kreisel, G. Principles of proof and ordinals implicit. in given concepts. in: Intuition­ ism and Proof Theory, edited by A. Kina, J. Myhill, and R. Vesley. North-Holland Publishing Company, 1970, pp. 489-516.

101. Kreisel, G. The formalist-positivist doctrine of mathematical precision in the light of experience. L' Age de la Science, vol. 3 (1970), pp. 17-45.

102. Kreisel, G. Hilbert's programme and the search for automatic proof procedures. in: Symposium on Authomatic Demonstration Held at Versailles/France, De­ cember 1968, edited by D. Lacombe, M. Laudet, L Nolin, and M. Schiitzenberger. Lecture Notes in Mathematics, vol. 125, Springer-Verlag, 1970, pp. 128-146.

103. Kreisel, G. and Troelstra, A. Formal systems for some branches of intuitionistic anal­ ysis. Annals of Mathematical Logic, vol. 3 (1971), pp. 437-439. An addendum.

104. Kreisel, G. Observations on popular discussions of foundations. in: Axiomatic Set Theory, Volume 1, edited by D. Scott. vol. 13, American Mathematical Society, Proceedings of Symposia.of Pure Mathematics, 1971, pp. 189-198.

105. Kreisel, G. and Krivine, J.-1. Elements of Mathematical Logic (Model Theory). North-Holland Publishing Company, 1971, xi+250 pp. [Second English edition).

106. Kreisel, G. Review of "The collected works of Gerhard Gentzen". Journal of Phi­ losophy, yol. 68 (1971 ), pp. 238-265.

8 107. Kreisel, G. Some reasons for generalizing recursiof!- theory. in: Logic Colloquium '69. Proceedings of the Summer School and Colloquium in Mathematical Logic, Manchester, August 1969, edited by R. Gandy and C. Yates. North­ Holland Publishing Company, 1971, pp. 139-198.

108. Kreisel, G. A survey of proof theory II. in: Proceedings of the Second Scandina­ vian Logic Symposium, edited by J. Fenstad. North-Holland Publishing Company, 1971, pp. 109-170.

109. Kreisel, G. Five Notes on the Application of Proof Theory to Computer Sci­ ence. Institute for Mathematical Studies in the Social Sciences, Stanford University, 1971, 45 pp. [Technical Report). llO. Kreisel, G. Bertrand Russell's logic. in: Bertrand Russell: A Collection of Critical Essays, edited by D. Pears. Doubleday, 1972, pp. 168-174.

111. Kreisel, G. and Zucker, J. Review of "Definition ein~s (relativ vollstandigen) formalen Systems konstruktiver Arithmetik". Journal of Symbolic Logic, vol. 37 (1972), pp. 203-204.

112. Kreisel, G. VVhich number theoretic problems can be solved in recursive progressions on IT~-paths through O? Journal of Symbolic Logic, vol. 37 (1972), pp. 311-334. 113. Kreisel, G. and Krivine, J. Modelltheorie. Eine Einfiihrung in die mathema­ tische Logik und Grundlagentheorie. Springer-Verlag, 1972, xv+274 pp. [First German edition].

114. Kreisel, G. Bertrand Arthur William Russell, Earl Russell 1872-1970. Biographical Memoirs of Fellows of the Royal Society, vol. ·19 (1973), pp. 583-620. ll5. Kreisel, G. Perspectives in the philosophy· of pure mathematics. in: Logic, Method­ ology and Philosophy.of Science IV, edited by P. Suppes, L. Henkin, G. Moisil, and A. Joja. North-Holland Publishing Company, :i973, pp. 255- 277.

116. Kreisel, G. and Takeuti, G. Formally self-referential propositions for cut free classical analysis and related systems. Dissertationes Mathematicae, vol. 118 (1974), pp. 1- 50.

117. Kreisel, G. Observations on a recent generalization of completeness theorems due to Schutte. in: I.S.I.L.C. Proof Theory Symposium University of Kiel 1974, Pro­ ceedings of the International Summer Institute and Logic Colloquium, edited by J. Diller and G. Muller. Lecture Notes in Mathematics, vol. 500, Springer­ Verlag, 1974, pp. 164-181.

118. Kreisel, G. What have we learnt from Hilbert 's second problem? in: Mathematical Developments Arising from Hilbert's Problerns, edited by F. Browder. vol. 28, American Mathematical Society, Proceedings of Symposia in Pure Mathematics, 197 4, pp. 93- 130.

9 119. Kreisel, G. Die formalistisch-positivistische Doktrin der mathematischen Priizision im Lichte der Erfahrung. in: Mathematiker iiber die Mathematik, edited by M. Otte. Springer-Verlag, 1974, pp. 64-123. (Revised German translation).

120. Kreisel, G. A notion of mechanistic theory. SynthP-se. An International Journal for Epistemology Methodology and Philosophy of Science, vol. 29 (1974), pp. 11-26.

121. Kreisel, G. Was hat die Logik in den letzten 25 Jahren fiir die Mathematik geleistet? Conceptus. Zeitschrift fiir Philosophie, vol. 9 (1975), pp. 40-45.

122. Kreisel, G., Mints, G., and Simpson, S. The use of abstract language in elementary metamathematics: Some pedagogic examples. in: Logic Colloquium: Symposium on Logic Held at Boston, 1972-1973, edited by R. Parikh. Lecture Notes in Mathematics, vol. 453, Springer-Verlag, 1975, pp. 38-131.'

123. Kreisel, G. Der unheilvolle Einbruch der Logik in die Mathematik. Acta Philosoph­ ica Fennica, vol. 28 (1976), pp. 166-187.

124. Kreisel, G. Relative consistency proofs II. The Journal of Symbolic Logic, vol. 41 (1976), pp. 285- 286. [Abstract].

125. Kreisel, G. A notion of mechanistic theory. in: Logi'c and Probability in Quantum Mechanics, edited by P. Suppes. D. Reidel Publishing Company, 1976, pp. 3-18. [Reprint).

126. Kreisel, G. ·Review of "L.E.J. Brouwer collected works} Volume I} Philosophy and foundations of mathematics". Bulletin of the American Mathematical Society, vol. 83 (1977), pp. 86-93.

127. Kreisel, G. Some uses of proof theory for finding computer programs. in: Colloques International de Logigue, Clermont-Ferrand, 18-25 Juillet 1975, edited by M. Guillaume. Centre National de la Recherche Scientifique, 1977, pp. 123-134.

128. Kreisel, G. Wie die Beweistheorie zu ihren Ordinalzahlen kam und kommt. Jahres­ bericht der Deutschen Mathematiker-Vereinigung, vol. 78 (1977), pp. 177-223.

129. Kreisel, G. On the kind of data needed for a theory of proofs. in: Logic Colloquium '76: Proceedings of a Conference Held in Oxford in July 1976, edited by R. Gandy and J. Hyland. North-Holland Publishing Company, 1977, pp. 111-128.

130. Kreisel, G. From foundations to science: Justifying and unwinding proofs. in: Sym­ posium: Set Theory. Foundations of Mathematics, edited by D. Kurepa. Math­ ematical Institute, 1977, pp. 63-72.

131. Kreisel, G. Review of "Wittgenstein's lectures on. the foundations of mathematics, Cambridge, 1939". BulJetin of the American Mathematical Society, vol. 84 (1978), pp. 79-90.

10 132. Kreisel, G. Some facts from the theory of proofs and some fictions from general proof theory. in: Essays on Mathematical and Philosophical Logic: Proceedings of the Fourth Scandivanian Logic Symposium and of the First Soviet-Finnish Logic Converence, edited by J. Hintikka, I. Niiniluoto, and E. Saarinen. D. Reidel Publishing Company, 1978, pp. 3-23.

133. Kreisel, G. The motto of 'Philosophical Investigations' and the philosophy of proofs and rules. Grazer Philosophische Studien, vol. 6 (1978), pp. 13-38.

134. Kreisel, G. Informal rigour and completeness proofs. in: II paradise di Cantor, edited by C. Cellucci. Bibliopolis, 1978, pp. 59-93. [Revised Italian translation).

135. Kreisel, G. Two notes on the foundations of set theory. in: II paradiso di Cantor, edited by C. Cellucci. Bibliopolis, 1978, pp. 97-120. [Revised Italian translation).

136. Kreisel, G. Zu Wittgensteins Gespri:ichen und Vorlesungen iiber die Grundlagen der Mathematik. in: Wittgenstein und sein Einfluss: auf die gegenwartige Philoso­ phie: Akten des 2. internationalen Wittgen~tein Symposiums 29. August bis 4. September 1977 in Kirchberg (Osterreich), edited by E, Leinfellner. Holder-Pichler-Tempsky, 1978, pp. 79-81.

137. Kreisel, G. Review of "Wittgenstein's Remarks on the Foundations of Mathematics". American Scientist, vol. 67 (1979), p. 619.

138. Kreisel, G. Formal rules and questions of justifying mathematical practice. in: Kon­ struktionen versus Positionen, edited by K. Lorenz. De Gruyter, 1979, pp. 99-130.

139. Kreisel, G. Review of "Comment on Zinoviev's paper". Logique et Analyse. Nou­ velle Serie, vol. 87 (1979), pp. 263-264.

140. Kreisel, G. Review of "Godel, Escher, Bach: An eternal golden braid". American Scientist, vol. 68 (1980): p. 200.

141. Kreisel, G. Kurt Godel. Biographical Memoirs of Fellows of the Royal Society, vol. 26 (1980), pp. 149-224.

142. Kreisel, G. Finitismus. in: Handbuch wissenschaftstheoretischer Begriffe, edited by J. Speck. Vandenhoeck & Ruprecht, 1980, pp. 233-234.

143. Kreisel, G. Grundlagen der Mathematik. in: Handbuch wissenschaftstheoretis­ cher Begriffe, edited by J. Speck. Vandenhoeck & Ruprecht, 1980, pp. 393-400.

144. Kreisel, G. Modell. in: Handbuch wissenschaftstheoretischer Begriffe, edited by J. Speck. Vandenhoeck & Ruprecht, 1980, pp. 437-440.

145. Kreisel, G. Modelltheorie. in: Handbuch wissenschaftstheoretischer Begriffe, edited by J. Speck. Vandenhoeck & Ruprecht, 1980, pp. 440-443.

11 146. Kreisel, G. Widersprunchsfreiheit. in: Handbuch wissenschaftstheoretischer Begriffe, edited by J. Speck. Vandenhoeck & Ruprecht, 1980, pp. 721-722.

147. Kreisel, G. Constructivistic approaches to logic. in: Modern Logic: A Survey, edited by E. Agazzi. D. Reidel Publishing Company, 1980, pp. 67-91.

148. Kreisel, G. Kurt Godel. Biographical Memoirs of Fellows of the Royal Society, vol. 27 (1981), p. 697. [Corrigenda]. '

149. Kreisel, G. A survey of proof theory. in: Issledovaniya po Teorii Dokazatel'stv (Investigations in Proof Theory), edited by S. Maslov. Matemateka Novoe v Zarubezhno'i' Nauke, vol. 23, Mir, 1981, pp. 9-113.

150. Kreisel, G. A survey of proof theory II. in: Issledovaniya po Teorii Dokazatel'stv (Investigations in Proof Theory), edited by S. Maslov. Matemateka Novoe v Zarubezhno'i' Nauke, vol. 23, Mir, 1981, pp. ll4-182. [Russian translation].

151. Kreisel, G. Wie die Beweistheorie zu ihren Ordinalzahlen kam und kommt. in: Issle­ dovaniya po Teorii Dokazatel'stv (Investigations in Proof Theory), edited by S. Maslov. Matemateka Novoe v Zarubezhno'i' Nauke, vol. 23, Mir, 1981, pp. 183-238. (Russian translation].

152. Kreisel, G. Some uses of proof theory for finding computer programs. in: Issle­ dovaniya po Teorii Dokazatel'stv (Investigations in Proof Theory), edited by S. Maslov. Matemateka Novoe v Zarubezhno'i' Nauke, vol. 23, Mir, 1981, pp. 239-256. [Russian translation].

153. Kreisel, G. On the kind of data needed for a theory of proofs. in: Issledovaniya po Teorii Dokazatel'stv (Investigations in Proof Theory), edited by S. Maslov. Matemateka Novoe v Zarubezhno'i' Nauke, vol. 23, Mir, 1981, pp. 257-287. (Rus­ sian translation].

154. Kreisel, G. Aussagenquantoren: Ein Beitrag der mathematischen Logik zur Erkennt­ nistheorie. in: Logik, Ethik und Sprache. Festschrift fiir Rudolf Freundlich, edited by K. Weinke. R. Oldenbourg Verlag, 1981, pp. 105-117.

155. Kreisel, G. Zur Bewertung mathematischer Definitionen. in: Philosophie als Wis­ senschaft. Essays in Scientific Philosophie, ed~ted by E. Morscher, 0. Neumaier, and G. Zecha. Comes Verlag, Bad Reichenhall, 1981, pp. 185-209.

156. Kreisel, G. Monadic operators defined by means of propositional quantification m intuitionistic logic. Reports on Mathematical Logic, vol. 12 (1981), pp. 9-15.

157. Kreisel, G. Neglected possibilities of processing assertions and proofs mechanically: Choice of problems and data. in: University-level Computer-assisted Instruc­ tion at Stanford, 1968-1980, edited by P. Suppes. Institute for Mathematical Studies in the Social Sciences, Stanford University, 1981, pp. 131-147.

12 158. Kreisel, G. Extraction of bounds: Interpreting some tricks of the trade. in: University-level Computer-assisted Instruction at Stanford, 1968-1980, edited by P. Suppes. Institute for Mathematical Studies in the Social Sciences, Stan­ ford University, 1981, pp. 149-163.

159. Kreisel, G. Kurt Godel. Biographical Memoirs of Fellows of the Royal Society, vol. 28 (1982), p. 719.

160. Kreisel, G. Review of "Brouwer's Cambridge lectures on intuitionism". Canadian Philosophical Review, vol. 2 (1982), pp. 249-251.

161. Kreisel, G. and Macintyre, A. Constructive logic versus algebraization I. in: The L.E.J. Brouwer Centenary Symposium, edited by D. van Dalen and A. Troelstra. North-Holland Publishing Company, 1982, pp. 217-260.

162. Kreisel, G. Finiteness theorems in arithmetic: An application of Herbrand 's theo­ rem for :B2 formulas. in: Proceedings of the Herbrand Symposium: Logic Colloquiu1n '81, Held in Marseilles, France, July 1981, edited by J. Stern. North-Holland Publishing Company, 1982, pp. 39-55.

163. Kreisel, G. Wittgenstein on rules and private language. Canadian Philosophical Review, vol. 3 (1983), pp. 287-289.

164. Kreisel, G. Einige Erlii:uterungen zu Wittgensteins Kummer mit Hilbert und Godel. in: Erkenntnis- und Wissenschaftstheorie: Akten des 7. internationalen Wittgenstein Symposiums 22. bix 29. August 1982, Kirchberg/Wechsel (Osterreich), edited by H. Czermak and P. Weingartner. Holder-Pichler-Tempsky, 1983, pp. 295-303.

165. Kreisel, G. Hilbert's program. in: Philosophy of Mathematics: Selected Read­ ings, (2nd edition), edited by P. Benacceraf and H. Putnam. Cambridge University Press, 1983, pp. 207-238. [Revised with a postscript].

166. Kreisel, G. Frege's foundations and intuitionistic logic. The Monist, vol. 67 (1984), pp. 71- 91.

167. Kreisel, G. Logical foundations: A lingering malaise: 1984. Department of Philosophy, Stanford University, 1984, 15 pp., [Text of a lecture delivered at Stanford University, June 1984].

168. Kreisel, G. After Frege 's Foundations: Beyond Informal Rigor. Department of Phi­ losophy, Stanford Univernity, 1984, 15 pp. [Preprint].

169. Kreisel, G. Review of "Fundamentals of generalized recursion theory". Bulletin (New Series) of the American Mathematical Society, vol. 13 (1985), pp. 183-196.

170. Kreisel, G. Philosophie: eine Erganzung der Wissenschaft? in: Die Aufgaben der Philosophie in der Gegenwart: Akten des 10. internationalen Wittgenstein

13 Symposiums, 18. bis 25. August 1985 in Kirchberg/Wechset (Osterreich), edited by vV. Leinfellner and F. Wuketits. Holder-Pichler-Tempsky, 1985, pp. 50-56.

171. Kreisel, G. Proof Theory and the Synthesis of Programs: Potential and Limitations. in: EUROCAL '85, European Conference on Computer Algebra, Linz, Aus­ tria, April 1-3 1985, Proceedings Volume 1: ; Invited Lectures, edited by B. Buchberger. vol. 203, Springer-Verlag, Lecture Notes in Computer Science, 1985, pp. 136-150.

172. Kreisel, G. Review of "Strukturtypen der Logik". Grazer Philosophische Studien, vol. 24 (1985), pp. 185-195.

173. Kreisel, G. li!fathematical logic: Tool and object lesson for science. Synthese, vol. 62 (1985), pp. 139-151.

174. Kreisel, G. Was hat die Wissenschaft von der mathematischen Logik'? m: Jahrbuch 1982 der Schweizerischen naturforschenden Gesellschaft, Vol­ ume I. Birkhauser, 1986, pp. 163- 173.

175. Kreisel, G. Proof Theory: some personal recollections. in: Proof Theory (second edition), edited by G. Takeuti. North-Holland, 1986, pp. 395-405.

176. Kreisel, G. Godel's excursions into intuitionistic logic. in: Godel Remembered, edited by P. Weingartner and L. Schmetterer. Bibliopolis, 1987, pp. 67-186.

177. Kreisel, G. Socalled Formal Reasoning and the Foundational Ideal. in: Logik, Wis­ senschaftstheorie und Erkenntnistheorie: Akten des 11. international~n Wittgenstein Symposiums 4. bis 13. August 1986 in Kirchberg/Wech~el (Osterreich), edited by P. Weingartner and G. Schurz. Holder-Pichler-Tempsky, 1987' pp. 19-42.

178. Kreisel, G. Church's thesis and the ideal of informal rigour. Notre Dame Journal of Formal Logic, vol. 28 (1987), pp. 499-519.

179. Kreisel, G. Valeur litteraire de la Pensee d'Aristote. m: Aristote aujourd'hui, edited by 11. Sinaceur. Unesco, Paris, 1988, pp. 20-21.

180. Kreisel, G. De la logique. in: Aristote aujourd'hui, edited by M. Sinaceur. Unesco, Paris, 1988, pp. 251-262.

181. Kreisel, G. Logique et mathematiques. in: Aristote aujourd'hui, edited by M. Sinaceur. Unesco, Paris, 1988, pp. 263-2~.

182. Kreisel, G. Review of "Kurt Godel, Collected Works, Volume I, Publications 1929- 1936". Notre Dame Journal of Formal Logic, yol. 29 (1988), pp. 160- 181. £ )'"..,. ~ o. : 3 o ( J q 8 'l) p. I !;I · 183. Kreisel, G. Kurt Godel (Part I). Uspekhi Mat.ematicheskikh Nauk, vol. 260 (1988), pp. 175-216. [Russian translation].

14 184. Kreisel, G. Kurr Godel (Part II). Uspekhi Matematicheskikh Nauk, vol. 261 (1988), pp. 203- 238. [Russian translation].

185. Kreisel, G. Zu Wittgensteins Sensibilitii.t. in: Traditionen und Perspektiven der Analyti­ schen ·Philosophie: Festschrift fiir Rudolf Haller, edited by W. Gombocz, H. Rutte, and W. Sauer. Holder-Pichler-Tempsky, 1989, pp. 203-223.

186. Kreisel, G. Zu einigen Gesprii.chen mit Wittgenstein: Erinnerungen und Gedanken. in: Wittgenstein: Biographie-Philosophie-Praxis, Wiener Secession 13. September bis 29. Oktober 1989. Catalogue to the exhibition, Vienna, 1989, pp. 131-143.

187. Kreisel, G. Logical aspects of the axiomatic method: on their significance in (traditional) logical foundations and in some (new) common-or-garden varieties of mathematics. iri: Logic Colloquium '87, edited by H.D. Ebbinghaus, J. Fernandez-Frida, M. Garrido, D. Lascar, and M. Artalejo. North-Holland Publishing Company, 1989, pp. 183-217.

188. Kreisel, G. Logical Aspects of Computation: Contributions and Distractions. in: Logic and Computer Science, edited by P. Odifreddi. APIC, vol. 31, Academic Press Ltd., 1990, pp. 205- 278.

189. Kreisel, G. Review of "Constructivism in mathematics: an introduction". Bull. London Math. Soc., vol. 22 (1990), pp. 505-511.

190. Kreisel, G. Review of "Kurt Godel, Collected Works, Vol. II". Notre Dame journai of Formal Logic, vol. 31 (1990), pp. 602-641.

191. Kreisel, G. Suitable descriptions for suitable categories. in: Advances in Scientific Philo­ sophy, edited by G. Schurz and G. Dorn. Rodopi, 1991, pp. 571-589.

192. Kreisel, G. Review of "Kurt Godel, Collected Works, Vol. II". Journal of Symbolic Logic, vol. 56 (1991), pp. 1085-1089.

193. Kreisel, G. On analogies in contemporary mathematics. in: Penser avec Aristote, edited by G. Hahn and M.A. Sinaceur. Eres, 1991, pp. 399-408.

194. Kreisel, G. Sur /es progres des sciences sociales depuis Aristote. in: Penser avec Aristote, edited by G. Hahn and M.A. Sinaceur. Eres, 1991, pp. 603-606.

195. Kreisel, G. On the idea(!) of logical closure. Annals of pure and applied logic, vol. 56 (1992), pp. 19-41. 15 I l - ......

196. Kreisel, G. Review of "Computability in Analysis and Physics". Jahresberichte der Deut­ schen Mathematiker-Vereinigung, vol. 94 (1992), pp. 53-55 (of the book reviews).

197. Kreisel, G. Le programme de Hilbert. in: Intuitionisme et theorie de la demonstration, edited by J. Largeault. J. Vrin, 1991, pp. 465-500.

198. Kreisel, G. A broader, not only professional view. Postscript to M. Baaz and P. Pudlak: Kreisel's conjecture for L31. in: Arithmetic, Proof Theory and Computational Com­ plexity, edited by P. Clote and J. Krajicek. Oxford University Press, 1993, pp. 50-60.

199.j Kreisel, G. Second thoughts around some of Gode l's writings: a non-academic option. Synthese vol. 114 (1998), pp. 99-160.