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 Gentzens and Novikovs, and provide a translation of the manuscript.
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