Volume 21, Issue 4, November 2017, Pages 640–655
A.-Roger LULA BABOLE1
1 Département de Mathématiques et Informatique, Université de Kinshasa, RD Congo
Original language: French
Copyright © 2017 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The GÖDEL’s theorem is intrinsically a theorem of limitation of the formals systems. The theorem shows that the coherence of PEANO’s arithmetic cannot be demonstrate by a simple way. This constitutes an opposite shock in metamathematic design in HILBERT’s perspective. Finally, if we want a proof of arithmetic coherence, it is sufficient to approve the arbitrary notions the type of function and function of function, and that next to concretes symbols.
Author Keywords: incompleteness, indecidability, demonstrability, truth, coherence.
A.-Roger LULA BABOLE1
1 Département de Mathématiques et Informatique, Université de Kinshasa, RD Congo
Original language: French
Copyright © 2017 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The GÖDEL’s theorem is intrinsically a theorem of limitation of the formals systems. The theorem shows that the coherence of PEANO’s arithmetic cannot be demonstrate by a simple way. This constitutes an opposite shock in metamathematic design in HILBERT’s perspective. Finally, if we want a proof of arithmetic coherence, it is sufficient to approve the arbitrary notions the type of function and function of function, and that next to concretes symbols.
Author Keywords: incompleteness, indecidability, demonstrability, truth, coherence.
Abstract: (french)
Le théorème de GÖDEL est intrinsèquement un théorème de limitation des systèmes formels. En tant que tel, il démontre que la cohérence de l’arithmétique de PEANO ne peut se montrer de façon élémentaire. Celui-ci constitue un contrecoup dans la métamathématique conçue dans la perspective hilbertienne : finitaire. Donc, si l’on veut une démonstration de la cohérence de l’arithmétique, il suffit d’admettre les notions abstraites du type de fonction et fonction de fonction, et cela à côté des symboles concrets.
Author Keywords: incomplétude, indécidabilité, démontrabilité, vérité, cohérence.
How to Cite this Article
A.-Roger LULA BABOLE, “THEOREME DE GODEL,” International Journal of Innovation and Applied Studies, vol. 21, no. 4, pp. 640–655, November 2017.
