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arXiv · 2006.08996

Lorenzen's proof of consistency for elementary number theory [with an edition and translation of "Ein halbordnungstheoretischer Widerspruchsfreiheitsbeweis'']

Thierry Coquand·Stefan Neuwirth
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Abstract

We present a manuscript of Paul Lorenzen that provides a proof of consistency for elementary number theory as an application of the construction of the free countably complete pseudocomplemented semilattice over a preordered set. This manuscript rests in the Oskar-Becker-Nachlass at the Philosophisches Archiv of Universit{\"a}t Konstanz, file OB 5-3b-5. It has probably been written between March and May 1944. We also compare this proof to Gentzen's and Novikov's, and provide a translation of the manuscript.

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Thierry Coquand, Stefan Neuwirth. 2020-06-16. Lorenzen's proof of consistency for elementary number theory [with an edition and translation of "Ein halbordnungstheoretischer Widerspruchsfreiheitsbeweis'']. https://doi.org/10.1080/01445340.2020.1752034

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