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.

中文翻译：

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Lorenzen 的初等数论一致性证明

我们展示了 Paul Lorenzen 的手稿，该手稿提供了初等数论的一致性证明，作为在预序集上构建自由可数完全伪补半格的应用。这份手稿保存在康斯坦茨大学哲学档案馆的 Oskar-Becker-Nachlass，文件 OB 5-3b-5。它可能写于 1944 年 3 月至 5 月之间。我们还将此证明与根岑和诺维科夫的证明进行了比较，并提供了手稿的翻译。