On the Question of Consistency of Arithmetic

¹ Mountain View, CA, USA

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.

KeywordsInconsistency and ConsistencyPeano ArithmeticNatural Deduction of PrawitzNormalization of Natural DeductionLanguageMinimal ArithmeticFinitary Arithmetic

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On the Question of Consistency of Arithmetic

Abstract

References (11)