Bulletin of the American Mathematical Society

MathSciNet review: 1567116
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Book Information:

Author: Kurt Schütte
Title: Proof theory
Additional book information: Grundlehren der Mathematischen Wissenschaften, Band 225, Springer-Verlag, Berlin, Heidelberg, New York, 1977, xii + 302 pp., $34.10.

Jane Bridge, A simplification of the Bachmann method for generating large countable ordinals, J. Symbolic Logic 40 (1975), 171–185. MR 398793, DOI 10.2307/2271898

2.

W. Buchholz, Eine Erweiterung der Schnitteliminations methode, Habilitationschrift, Ludwig-Maximilians-Universität, München, 1977.

Solomon Feferman, Formal theories for transfinite iterations of generalized inductive definitions and some subsystems of analysis, Intuitionism and proof theory (Proc. Conf., Buffalo, N.Y., 1968) North-Holland, Amsterdam, 1970, pp. 303–326. MR 0302424

4.

S. Feferman, Review of [12], Bull. Amer. Math. Soc. 83 (1977), 351-361. (Note: [F2] of the references of [4] has now appeared in the Handbook of mathematical logic (J. Barwise, ed.), North-Holland, Amsterdam, 1970, pp. 913-971.)

Harvey Friedman, Iterated inductive definitions and $\Sigma _{2}^{1}-\textrm {AC}$, Intuitionism and Proof Theory (Proc. Conf., Buffalo, N.Y., 1968) North-Holland, Amsterdam, 1970, pp. 435–442. MR 0284326

J. Y. Girard, Three-valued logic and cut-elimination: the actual meaning of Takeuti’s conjecture, Dissertationes Math. (Rozprawy Mat.) 136 (1976), 49. MR 446918

7.

W. Pohlers, Beweistheorie der iterierten Induktiven Definitionen, Habilitationschrift, Ludwig-Maximilians-Universität, München, 1977.

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

9.

W. Sieg, Trees in metamathematics: theories of inductive definitions and subsystems of analysis, Dissertation, Stanford Univ. 1977.

10.

S. Stenlund, Combinators, λ-terms and proof theory, Reidel, Dordrecht, 1972.

W. W. Tait, Infinitely long terms of transfinite type, Formal Systems and Recursive Functions (Proc. Eighth Logic Colloq., Oxford, 1963) North-Holland, Amsterdam, 1965, pp. 176–185. MR 0195727

Gaisi Takeuti, Proof theory, 2nd ed., Studies in Logic and the Foundations of Mathematics, vol. 81, North-Holland Publishing Co., Amsterdam, 1987. With an appendix containing contributions by Georg Kreisel, Wolfram Pohlers, Stephen G. Simpson and Solomon Feferman. MR 882549

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

1.

J. Bridge, A simplification of the Bachmann method for generating large countable ordinals, J. Symbolic Logic 40 (1975), 171-185. MR 0398793

2.

W. Buchholz, Eine Erweiterung der Schnitteliminations methode, Habilitationschrift, Ludwig-Maximilians-Universität, München, 1977.

3.

S. Feferman, Formal theories for transfinite iterations of generalized inductive definitions and some subsystems of analysis, Intuitionism and Proof Theory, North-Holland, Amsterdam, 1970, pp. 303-325. MR 302424

4.

S. Feferman, Review of [12], Bull. Amer. Math. Soc. 83 (1977), 351-361. (Note: [F2] of the references of [4] has now appeared in the Handbook of mathematical logic (J. Barwise, ed.), North-Holland, Amsterdam, 1970, pp. 913-971.)

5.

H. Friedman, Iterated inductive definitions and $\Sigma \sb{2}\sp{1}-{\rm AC}$, Intuitionism and Proof Theory, North-Holland, Amsterdam, 1970, pp. 435-442. MR 284326

6.

J.-Y. Girard, Three-valued logic and cut-elimination: the actual meaning of Takeuti's conjecture, Dissertationes Math. 136 (1976). MR 446918

7.

W. Pohlers, Beweistheorie der iterierten Induktiven Definitionen, Habilitationschrift, Ludwig-Maximilians-Universität, München, 1977.

8.

K. Schutte, Beweistheorie, Springer-Verlag, Berlin, 1960. MR 118665

9.

W. Sieg, Trees in metamathematics: theories of inductive definitions and subsystems of analysis, Dissertation, Stanford Univ. 1977.

10.

S. Stenlund, Combinators, λ-terms and proof theory, Reidel, Dordrecht, 1972.

11.

W. W. Tait, Infinitely long terms of transfinite type, Formal Systems and Recursive Functions (Crossley and Dummett, eds.), North-Holland, Amsterdam, 1965, pp. 465-475. MR 195727

12.

G. Takeuti, Proof theory, North-Holland, Amsterdam, 1975. MR 882549

13.

A. S. Troelstra (Editor), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Math., vol, 344, Springer-Verlag, Berlin, 1973. MR 325352