Bulletin of the American Mathematical Society

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Book Information:

Author: Gaisi Takeuti
Title: Proof theory
Additional book information: Studies in Logic and the Foundations of Mathematics, vol. 81, North-Holland/American Elsevier, Amsterdam, Oxford, New York, 1975, vii + 372 pp., $35.50.

Errett Bishop, Foundations of constructive analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221878

Solomon Feferman, Lectures on proof theory, Proceedings of the Summer School in Logic (Leeds, 1967) Springer, Berlin, 1968, pp. 1–107. MR 0235996

[F2] S. Feferman, Theories of finite type related to mathematical practice, Handbook of Mathematical Logic (to appear).

Gerhard Gentzen, The collected papers of Gerhard Gentzen, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam-London, 1969. Edited by M. E. Szabo. MR 0262050

Jacques Herbrand, Logical writings, Harvard University Press, Cambridge, Mass., 1971. A translation of the Écrits logiques, edited by Jean van Heijenoort and including contributions by Claude Chevalley and Albert Lautman. MR 0366597

D. Hilbert and P. Bernays, Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, Band 50, Springer-Verlag, Berlin-New York, 1970 (German). Zweite Auflage. MR 0272596

A. Kino, J. Myhill, and R. E. Vesley (eds.), Intuitionism and proof theory (Proceedings of the Summer Conference at Buffalo, N. Y., 1968), Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., Amsterdam-London, 1970. MR 0270891

G. Kreisel, A survey of proof theory, J. Symbolic Logic 33 (1968), 321–388. MR 281580, DOI 10.2307/2270324

G. Kreisel, A survey of proof theory. II, Proc. Second Scandinavian Logic Sympos. (Oslo, 1970) Studies in Logic and the Foundations of Mathematics, Vol. 63, North-Holland, Amsterdam, 1971, pp. 109–170. MR 0424533

G. Kreisel, What have we learnt from Hilbert’s second problem?, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc., Providence, R.I., 1976, pp. 93–130. MR 0434781

Dag Prawitz, Natural deduction. A proof-theoretical study, Acta Universitatis Stockholmiensis. Stockholm Studies in Philosophy, vol. 3, Almqvist & Wiksell, Stockholm, 1965. MR 0193005

[PTS] Proof theory symposium (Kiel, 1974) (Diller and Müller, Editors), Lecture Notes in Math., vol. 500, Springer-Verlag, Berlin and New York, 1975.

Kurt Schütte, Beweistheorie, Die Grundlehren der mathematischen Wissenschaften, Band 103, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960 (German). MR 0118665

J. E. Fenstad (ed.), Proceedings of the Second Scandinavian Logic Symposium, Studies in Logic and the Foundations of Mathematics, Vol. 63, North-Holland Publishing Co., Amsterdam-London, 1971. Held at the University of Oslo, Oslo, June 18–20, 1970. MR 0317876

A. S. Troelstra (ed.), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Mathematics, Vol. 344, Springer-Verlag, Berlin-New York, 1973. MR 0325352

Jean van Heijenoort, From Frege to Gödel. A source book in mathematical logic, 1879–1931, Harvard University Press, Cambridge, Mass., 1967. MR 0209111

[B] E. Bishop, Foundations of constructive analysis, McGraw-Hill, New York, 1967. MR 36 #4930. MR 0221878




[F1] S. Feferman, Lectures on proof theory, Proc. Summer School in Logic (Leeds, 1967), Lecture Notes in Math., vol. 70, Springer-Verlag, Berlin and New York, 1968, pp. 1-107. MR 38 #4294. MR 235996




[F2] S. Feferman, Theories of finite type related to mathematical practice, Handbook of Mathematical Logic (to appear).




[G] The collected papers of Gerhard Gentzen (M. E. Szabo, Editor), North-Holland, Amsterdam and London, 1969. MR 41 #6660. MR 262050




[H] J. Herbrand, Logical writings (W. D. Goldfarb, Editor), Harvard Univ. Press, Cambridge, Mass., 1971. MR 51 #2844. MR 366597




[H, B] D. Hilbert and P. Bernays, Grundlagen der Mathematik. II, 2nd ed., Springer-Verlag, Berlin and New York, 1970. MR 42 #7477. MR 272596




[IPT] Intuitionism and proof theory (A. Kino, J. Myhill and R. E. Vesley, Editors), Proc. Summer Conf., Buffalo, New York, 1968, North-Holland, Amsterdam and London, 1970. MR 42 #5774. MR 270891




[K1] G. Kreisel, A survey of proof theory. I, J. Symbolic Logic 33 (1968), 321-388. MR 43 #7295. MR 281580




[K1] G. Kreisel, A survey of proof theory. II, Proc. Second Scandinavian Logic Sympos. (Oslo, 1970), North-Holland, Amsterdam and London, 1971, pp. 109-170. MR 47 #6425. MR 424533




[K2] G. Kreisel, what have we learnt from Hilbert's second problem? Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc., Providence, R.I., 1976, pp. 93-130. MR 434781




[P] D. Prawitz, Natural deduction, a proof-theoretical study, Almqvist and Wiksell, Stockholm, 1965. MR 33 #1227. MR 193005




[PTS] Proof theory symposium (Kiel, 1974) (Diller and Müller, Editors), Lecture Notes in Math., vol. 500, Springer-Verlag, Berlin and New York, 1975.




[S] K. Schütte, Beweistheorie, Springer-Verlag, Berlin, 1960. MR 22 #9438. MR 118665




[SL] Proc. Second scandinavian logic symposium (Oslo, 1970) (J. E. Fenstad, Editor), North-Holland, Amsterdam and London, 1971. MR 47 #6425. MR 317876




[T] A. S. Troelstra (Editor), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Math., vol. 344, Springer-Verlag, Berlin and New York, 1973. MR 48 #3699. MR 325352




[Vh] J. van Heijenoort, From Frege to Gödel. A source book in mathematical logic, 1879-1931, Harvard Univ. Press, Cambridge, Mass., 1967. MR 35 #15. MR 209111