Logical Approaches to Computational Barriers

Computable counter-examples to the Brouwer fixed-point theorem

Speaker:
| Petrus H. Potgieter |

Slot: |
Array, 12:00-12:20, 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 KÃ¶nig lemma in RCA$_0$ (the system of recursive comprehension) and this result is illustrated by relating the weak KÃ¶nig lemma directly to the Baigger example.

websites: Arnold Beckmann | 2008-06-11 |