The Formalization of The Arithmetic System on The Ground of The Atomic Logic

Abstract

This paper is a continuation of the paper [16]. Namely, in [16] we have introduced, among others, the definition of the atomic entailment and we have constructed the system $\stackrel{\sqcap }{S}$, which is based on the atomic entailment. In this paper we show that the classical Arithmetic can be based on the Atomic Logic (see [17]).

The paper: T.J. Stepien, L.T. Stepien, "Atomic Entailment and Atomic Inconsistency and Classical Entailment", cited in this paper, as [16], was also published in arXiv, as arXiv:1603.06621