Volume 21, Issue 1, August 2017, Pages 103–123
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 resort in arithmetization of arithmetic reaches to construct inside of arithmetic a proposition which confirm its self-indemonstrability. In substance, the proof of coherence presupposes a form of induction in transfinite order for proving the coherence of arithmetic which is the finite order. It is dealing recursive functions which have the properties for all attribute values system to determine them by the means of finite type procedure. It comes to recursive arithmetic, to translate the elements of metatheory formal system.
Author Keywords: arithmetization, metatheory, recursivity, recursive arithmetic, iteration, metamathematic, incompletenes.
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 resort in arithmetization of arithmetic reaches to construct inside of arithmetic a proposition which confirm its self-indemonstrability. In substance, the proof of coherence presupposes a form of induction in transfinite order for proving the coherence of arithmetic which is the finite order. It is dealing recursive functions which have the properties for all attribute values system to determine them by the means of finite type procedure. It comes to recursive arithmetic, to translate the elements of metatheory formal system.
Author Keywords: arithmetization, metatheory, recursivity, recursive arithmetic, iteration, metamathematic, incompletenes.
Abstract: (french)
Le recours à l’arithmétisation de l’arithmétique amène à construire à l’intérieur de l’arithmétique une proposition qui affirme sa propre indémontrabilité. Au fond, la preuve de la cohérence présuppose une forme d’induction de l’ordre transfini aux fins de prouver la cohérence de l’arithmétique qui est de l’ordre fini. Il s’agit donc des fonctions récursives qui ont des propriétés pour tout système de valeurs attribué à ses arguments de les déterminer aux moyens d’une procédure de type fini. Il revient à l’arithmétique récursive de traduire les éléments de la métathéorie du système formel.
Author Keywords: Arithmétisation, métatheorie, récursivité, arithmétique récursive, itération, métamathématique, incomplétude.
How to Cite this Article
A.-Roger LULA BABOLE, “L’arithmétisation et la métathéorie,” International Journal of Innovation and Applied Studies, vol. 21, no. 1, pp. 103–123, August 2017.
