Semi-Formal Calculi and Their Applications

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

A chapter in Gentzen's Centenary, 2015, pp 317-354 from Springer

Abstract: 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.

Keywords: Semi-formal System; Gentzen; Verification Calculus; Countably Infinite Structure; Finiteness Theorem (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10103-3_13

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DOI: 10.1007/978-3-319-10103-3_13

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