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On the Question of Consistency of Arithmetic

DOI: 10.4236/apm.2026.161003, PP. 29-44

Keywords: Inconsistency and Consistency, Peano Arithmetic, Natural Deduction of Prawitz, Normalization of Natural Deduction, Language , Minimal Arithmetic, Finitary Arithmetic

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Abstract:

A system of finitary arithmetic is introduced, and a proof for its consistency is proposed. It is shown that the proof of the consistency of finitary arithmetic, formalized in Peano arithmetic, implies the consistency of Peano arithmetic. Due to the results of the article, Peano arithmetic should be suspected of being inconsistent.

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