Refining the arithmetical hierarchy of classical principles

TL;DR

This paper refines the arithmetical hierarchy of classical logical principles by analyzing their derivability relations within Heyting arithmetic, focusing on specific logical laws and principles.

Contribution

It provides a detailed classification of classical principles based on their derivability over Heyting arithmetic, including restricted versions of key logical laws.

Findings

Identifies derivability relations among classical principles

Classifies principles based on their logical strength

Provides a refined hierarchy of classical logical principles

Abstract

We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, de Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.