Individual choice sequences -- History, development and use

TL;DR

This paper traces the historical development of Brouwer's use of individual choice sequences, analyzing their application and Brouwer's subsequent work with a focus on foundational principles and proof explanations.

Contribution

It provides a detailed historical and analytical reconstruction of Brouwer's use of choice sequences, grounded in basic principles and aligned with his post-1927 work.

Findings

Clarifies Brouwer's application of choice sequences

Provides a foundational explanation of Brouwer's proofs

Aligns historical development with Brouwer's later work

Abstract

We follow the history and development of Brouwer's use of individual choice sequences up to the discovery of a method to apply them successfully in 1927. With the principles we derive from this first use we analyze in detail Brouwer's work from that time onward. Our reconstruction uses only very basic principles. It aligns exactly with Brouwer's work after 1927 and, moreover, it gives a clear explanation of the proofs of his results and the terms he uses.