Computability in Europe 2008
Logic and Theory of Algorithms

Regular Talk:
Computable counter-examples to the Brouwer fixed-point theorem

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Speaker:	Petrus H. Potgieter
Slot:	Tue, 12:00-12:20, Amphitheater A (col. 1)

Abstract

This paper is an overview of results that show the Brouwer fixed-point theorem (BFPT) to be essentially non-constructive and non-computable. The main results, the counter-examples of Orevkov and Baigger, imply that there is no procedure for finding the fixed point in general by giving an example of a computable function which does not fix any computable point. Research in reverse mathematics has shows the BFPT to be equivalent to the weak König lemma in RCA$_0$ (the system of recursive comprehension) and this result is illustrated by relating the weak König lemma directly to the Baigger example.