Computability in Europe 2008
Logic and Theory of Algorithms
|Speaker:||Petrus H. Potgieter|
|Slot:||Tue, 12:00-12:20, Amphitheater A (col. 1)|
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.
|websites: Arnold Beckmann||2008-06-11|