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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. J. Bridge, A simplification of the Bachmann method for generating large countable ordinals, J. Symbolic Logic 40 (1975), 171-185. MR 398793
  • 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. 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 (Editor), Metamathematical investigation of intuitionistic arithmetic and analysis, Lecture Notes in Math., vol, 344, Springer-Verlag, Berlin, 1973. MR 325352

Review Information:

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