History and Philosophy of Logic:1-10 (forthcoming)

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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DOI 10.1080/01445340.2020.1752034
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Proof Theory in the USSR 1925–1969.Grigori Mints - 1991 - Journal of Symbolic Logic 56 (2):385-424.
Calculuses and Formal Systems.Haskell B. Curry - 1958 - Dialectica 12 (3‐4):249-273.

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