On the Performance of Axiom Systems

Wolfram Pohlers ()
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Wolfram Pohlers: Institut für Mathematische Logik und Grundlagenforschung

Chapter Chapter 3 in Axiomatic Thinking II, 2022, pp 35-88 from Springer

Abstract: Abstract One of the aims of proof theory is to calibrate the strength of axiom systems by invariants. According to Gödel’s discoveries these invariants will in general not be finite but rather transfinite objects. Pioneering work in this direction had been done by Gerhard Gentzen who characterized the axiom system for Peano arithmetic by the transfinite ordinal $${\varepsilon _0}$$ ε 0 . In this paper we try to develop a general framework for characterizing ordinals of axiom systems and study to what extend these ordinals embody a measure for their performance.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-77799-9_3

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DOI: 10.1007/978-3-030-77799-9_3

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