Number Theory


A Technical Report on 'The Inconsistency of Arithmetic'

Authors: David Streit, Christoph Benzmüller

The present paper is a technical report on 'The Inconsistency of Arithmetic' available on It contains a formalized analysis where the authors claim to "constitute a verified proof document" by an automated verification using the proof assistant 'Isabelle / HOL'. In order to refute the key statement (II) on page 2 of the inconsistency proof, the authors seek to create a countermodel. However, this model is based on an erroneous application of predicate logic. The crucial point is the lemma on page 7 which is proved wrongly. For that statement becoming true, the two sets S1, S2 have to exist for the case that (G) is true and for the case that (G) is false, and not the other way around: if (G) is true there is a pair of unequal sets that does the job and if (G) is false there is another pair.

Comments: 12 Pages.

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Submission history

[v1] 2019-10-08 07:07:54

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