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Normal derivability in classical logic

Part of the Lecture Notes in Mathematics book series (LNM,volume 72)

Keywords

  • Propositional Logic
  • Normal Derivation
  • Axiom System
  • Peano Arithmetic
  • Predicate Variable

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References

  1. Barwise, J., Infinitary logic and admissible sets, J. Symbolic Logic, to appear.

    Google Scholar 

  2. Feferman, S., Systems of predicative analysis, Journal of Symbolic Logic, vol. 29 (1964), pp. 1–30.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Gentzen, G., Untersuchungen über das logische Schlussen, Mathematische Zeitschrift, vol. 39 (1935), pp. 176–221.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. -, Die Widerspruchspreiheit der reinen Zahlentheorie, Mathematische Annalen, vol. 112 (1936), pp. 403–565.

    CrossRef  MathSciNet  Google Scholar 

  5. -, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Mathematische Annalen, vol. 119 (1943), pp. 140–161.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Karp, C. R., Languages with expressions of infinite length, Amsterdam, 1964.

    Google Scholar 

  7. Lopez-Escobar, E. G. K., An interpolation theorem for denumerably long formulas, Fundamenta Mathematicae, LVII (1965).

    Google Scholar 

  8. Lorenzen, P., Algebraische und logistische Untersuchungen über freie Verbände, Journal of Symbolic Logic, vol. 16 (1951), pp. 81–106.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Schütte, K., Beweistheoretische Erfassung der unendlichen Induktion in der Zahlentheorie, Mathematische Annalen, vol. 122, (1955), pp. 369–389.

    CrossRef  MATH  Google Scholar 

  10. -, Kennzeichnung von Ordnungszahlen durch rekursiv erklärte Funktionen, Mathematische Annalen, vol. 127, (1954), pp. 13–32.

    CrossRef  MATH  Google Scholar 

  11. Schütte, K., Beweistheorie, Berlin, Gottingen, Heidelberg, 1960.

    Google Scholar 

  12. Schütte, K., Predicative well-orderings, Formal Systems and Recursive Functions, Amsterdam 1965, pp. 280–303.

    Google Scholar 

  13. Schütte, K., Eine Grenze für die Beweisbarkeit der transfiniten Induktion in der verzweigten Typenlogic, Archiv fur Mathematische Logik und Grundlagenferschung, vol. 7, pp. 45–60.

    Google Scholar 

  14. Tait, W. W., Cut elimination in infinite propositional logic (Abstract), Journal of Symbolic Logic, vol. 31, (1966), p. 151.

    Google Scholar 

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© 1968 Springer-Verlag

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Tait, W.W. (1968). Normal derivability in classical logic. In: Barwise, J. (eds) The Syntax and Semantics of Infinitary Languages. Lecture Notes in Mathematics, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079691

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  • DOI: https://doi.org/10.1007/BFb0079691

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04242-6

  • Online ISBN: 978-3-540-35900-5

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