Lorenzen's Proof of Consistency for Elementary Number Theory. Issue 3 (2nd July 2020)

• Record Type: Journal Article
• Authors: Coquand, Thierry; Neuwirth, Stefan
• Is Part Of: History and philosophy of logic. Volume 41:Issue 3(2020)
• Page Start: 281
• Page End: 290
• Publication Date: 2020-07-02
• Subjects: Logic -- Periodicals; 160.905
• DOI: 10.1080/01445340.2020.1752034
• Languages: English
• ISSNs: 0144-5340

Abstract

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.