Paraconsistent second order arithmetic Z^#_2 based on the paraconsistent logic LP^# with infinite hierarchy levels of contradiction. Berry's and Richard's inconsistent numbers within Z^#_2

TL;DR

This paper introduces a paraconsistent second order arithmetic system Z#2 based on LP# logic, incorporating infinite hierarchy levels of contradiction, and defines inconsistent numbers within this framework.

Contribution

It develops a novel paraconsistent arithmetic system Z#2 with an unrestricted comprehension scheme and constructs infinite hierarchy of inconsistent numbers.

Findings

Defined paraconsistent field R^# with inconsistent numbers

Developed portions of paraconsistent mathematics within Z#2

Outlined the hierarchy of contradictions in the system

Abstract

In this paper paraconsistent second order arithmetic Z#2 with unrestricted comprehension scheme is proposed. We outline the development of certain portions of paraconsistent mathematics within paraconsistent second order arithmetic Z#2.In particular we defined infinite hierarchy Berry's and Richard's inconsistent numbers as elements of the paraconsistent field R^#.