Volume 21, Issue 1, August 2017, Pages 137–152
A.-Roger LULA BABOLE1, Alain MUSESA LANDA2, and Oscar LUNGIAMBUDILA MAMONA3
1 Département de Mathématiques et Informatique, Université de Kinshasa, RD Congo
2 Département des Mathématiques et Informatique, Université de , RD Congo
3 Département des Mathématiques et Informatique, Université de , 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 study presents systematically the formals and theoretical foundations of incompleteness theorem: framework, hypothesis, rules of provability. The recursive functions constitute the operational foundations in the development, the construction and the prove of this theorem. The preparatory theorems and the sense theorem are the socle which establishes the incompleteness.
Author Keywords: sense theorem, recursive functions, expansivity, recessivity, diagonal argument.
A.-Roger LULA BABOLE1, Alain MUSESA LANDA2, and Oscar LUNGIAMBUDILA MAMONA3
1 Département de Mathématiques et Informatique, Université de Kinshasa, RD Congo
2 Département des Mathématiques et Informatique, Université de , RD Congo
3 Département des Mathématiques et Informatique, Université de , 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 study presents systematically the formals and theoretical foundations of incompleteness theorem: framework, hypothesis, rules of provability. The recursive functions constitute the operational foundations in the development, the construction and the prove of this theorem. The preparatory theorems and the sense theorem are the socle which establishes the incompleteness.
Author Keywords: sense theorem, recursive functions, expansivity, recessivity, diagonal argument.
Abstract: (french)
L’étude présente systématiquement et méthodiquement les fondements théoriques et formels du théorème d’incomplétude : cadre, hypothèses, règles de prouvabilité. Les fonctions récursives constituent et servent de soubassements opératoires dans le développement, la construction et la preuve dudit théorème. Les théorèmes préparatoires et le théorème du sens sont les socles établissant l’incomplétude.
Author Keywords: théorème, du sens, fonctions récursives, expansivité, récessivité, argument diagonal.
How to Cite this Article
A.-Roger LULA BABOLE, Alain MUSESA LANDA, and Oscar LUNGIAMBUDILA MAMONA, “Bases logiques de l’incomplétude,” International Journal of Innovation and Applied Studies, vol. 21, no. 1, pp. 137–152, August 2017.
