Copies of classical logic in intuitionistic logic

TL;DR

This paper demonstrates that there are multiple distinct ways to embed classical logic within intuitionistic logic, challenging the assumption of a unique copy and expanding understanding of their relationship.

Contribution

It introduces three different embeddings of classical logic into intuitionistic logic, showing the non-uniqueness of such copies.

Findings

Identifies three distinct embeddings of classical logic in intuitionistic logic

Challenges the assumption that all copies are the same

Expands understanding of the relationship between classical and intuitionistic logic

Abstract

Classical logic (the logic of non-constructive mathematics) is stronger than intuitionistic logic (the logic of constructive mathematics). Despite this, there are copies of classical logic in intuitionistic logic. All copies usually found in the literature are the same. This raises the question: is the copy unique? We answer negatively by presenting three different copies.