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Semi-Formal Calculi and Their Applications

In: Gentzen's Centenary

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  • Wolfram Pohlers

    (Institut für Mathematische Logik und Grundlagenforschung, Westfälische Wilhelms—Universität)

Abstract

By a semi-formal system we understand a proof system which includes infinitary inference rules. The use of inference rules with infinitely many premises was already suggested by David Hilbert in his paper “Die Grundlegung der elementaren Zahlentheorie” [6] and was later systematically used by Kurt Schütte in his work on proof theory. The heigths of proof trees in a semi-formal system are canonically measured by ordinals. Therefore, in contrast to Gentzen’s original approach, ordinals enter proof theoretic research via semi-formal systems in a completely canonical way.

Suggested Citation

  • Wolfram Pohlers, 2015. "Semi-Formal Calculi and Their Applications," Springer Books, in: Reinhard Kahle & Michael Rathjen (ed.), Gentzen's Centenary, edition 1, pages 317-354, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-10103-3_13
    DOI: 10.1007/978-3-319-10103-3_13
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