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International Journal of Innovation and Applied Studies
ISSN: 2028-9324     CODEN: IJIABO     OCLC Number: 828807274     ZDB-ID: 2703985-7
 
 
Thursday 17 August 2017

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L’arithmétique formelle et l’incomplétude


Volume 21, Issue 1, August 2017, Pages 96–102

 L’arithmétique formelle et l’incomplétude

A.-Roger LULA BABOLE1 and Yves MANGONGO TINDA2

1 Département des Mathématiques et Informatique, Université de Kinshasa, RD Congo
2 Département des Mathématiques et Informatique, Université de Kinshasa, RD Congo

Original language: French

Received 22 February 2017

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


By applying the formal arithmetic model, the mathematic and logic theories have created the self-references and have chosen a specific model for accomplish the logic-mathematics proves. A formal arithmetic (ROBINSON et PEANO) constitute in this fact the basic hypothesis for the two incompleteness theorems.

Author Keywords: formal arithmetic, incompleteness, decidability, axiomatic, coherence.


Abstract: (french)


En appliquant le modèle de l’arithmétique formelle, les théories mathématiques et logiques ont créé les autoréférences et ont choisi un modèle spécifique pour faire assoir les preuves logico-mathématiques. L’arithmétique formelle (ROBINSON et PEANO) constitue, à cet effet, les hypothèses de base de deux théorèmes d’incomplétude.

Author Keywords: Arithmétique formelle, incomplétude, décision, axiomatique, cohérence.


How to Cite this Article


A.-Roger LULA BABOLE and Yves MANGONGO TINDA, “L’arithmétique formelle et l’incomplétude,” International Journal of Innovation and Applied Studies, vol. 21, no. 1, pp. 96–102, August 2017.