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Bulletin of the American Mathematical Society

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Book Review

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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.

References [Enhancements On Off] (What's this?)

  • 1. Jane 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. 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.)
  • 5. Harvey Friedman, Iterated inductive definitions and Σ₂¹-𝐴𝐶, Intuitionism and Proof Theory (Proc. Conf., Buffalo, N.Y., 1968) North-Holland, Amsterdam, 1970, pp. 435–442. MR 0284326
  • 6. J. Y. Girard, Three-valued logic and cut-elimination: the actual meaning of Takeuti’s conjecture, Dissertationes Math. (Rozprawy Mat.) 136 (1976), 49. MR 0446918
  • 7. W. Pohlers, Beweistheorie der iterierten Induktiven Definitionen, Habilitationschrift, Ludwig-Maximilians-Universität, München, 1977.
  • 8. Kurt Schütte, Beweistheorie, Die Grundlehren der mathematischen Wissenschaften, Bd. 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.
  • 11. W. W. Tait, Infinitely long terms of transfinite type, Formal Systems and Recursive Functions (Proc. Eighth Logic Colloq., Oxford, North-Holland, Amsterdam, 1965, pp. 176–185. MR 0195727
  • 12. 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
  • 13. 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

Review Information:

Reviewer: Solomon Feferman
Journal: Bull. Amer. Math. Soc. 1 (1979), 224-228