Retracing Cantor's first steps in Brouwer's company

TL;DR

This paper establishes intuitionistic versions of classical theorems, demonstrating that all countable closed subsets of a specific interval are sets of uniqueness, thus extending classical results into an intuitionistic framework.

Contribution

It introduces intuitionistic proofs for classical theorems about countable closed subsets being sets of uniqueness, bridging classical and intuitionistic analysis.

Findings

Countable closed subsets of [-π,π] are sets of uniqueness in the intuitionistic setting.

Extension of classical theorems into intuitionistic analysis.

Provides new insights into the structure of countable sets in constructive mathematics.

Abstract

We prove intuitionistic versions of the classical theorems saying that all countable closed subsets of $[-\pi,\pi]$ and even all countable subsets of $[-\pi,\pi]$ are sets of uniqueness.