Lorenzen's Proof of Consistency for Elementary Number Theory

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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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10.1080/01445340.2020.1752034

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Author Profiles

Thierry Coquand
Stefan Neuwirth
Université de Franche-Comté

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From Frege to Gödel.Jean van Heijenoort - 1968 - Philosophy of Science 35 (1):72-72.
Die Widerspruchsfreiheit der reinen Zahlentheorie.Gerhard Gentzen - 1936 - Journal of Symbolic Logic 1 (2):75-75.
The theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.

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