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Proof Theory

  • Kurt Schütte
Part of the Synthese Library book series (SYLI, volume 149)

Abstract

Proof theory was established at first by David Hilbert to gain a foundation of classical mathematics by very elementary methods which he called finitary (finit). The idea was to formalize the particular parts of classical mathematics and to prove the consistency of the corresponding formal systems only in a syntactical way without reference to the intended meanings of the formal systems.

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Bibliography

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    Feferman, S., ‘Systems of Predicative Analysis’, J. Symbolic Logic 29 (1964), 1–30.CrossRefGoogle Scholar
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    Gödel, K., ‘Über eine bisher noch nicht beniitzte Erweiterung des finiten Standpunktes’, Dialectica 12 (1958), 280–287.CrossRefGoogle Scholar
  3. [3]
    Hilbert, D. and Bernays, P., Grundlagen der Mathematik I, II, Springer-Verlag, Heidelberg, New York 1968, 1970.Google Scholar
  4. [4]
    Schütte, K., Proof Theory, Springer-Verlag, Berlin, Heidelberg, New York 1977.Google Scholar
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    Spector, C., ‘Provably Recursive Functional of Analysis: A Consistency Proof of Analysis by an Extension of Principles Formulated in Current Intuitionistic Mathematics’, Proc. Symp. Pure Math. AMS V (1962), 1–27.Google Scholar
  6. [6]
    Takeuti, G., Proof Theory, North-Holland Publ. Co., Amsterdam 1975.Google Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Kurt Schütte
    • 1
  1. 1.MunichGermany

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