Lorenzen's Proof of Consistency for Elementary Number Theory

History and Philosophy of Logic 41 (3):281-290 (2020)
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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 Universität 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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Stefan Neuwirth
Université de Franche-Comté

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