Individual choice sequences -- History, development and use

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.