Research ArticleOpen accessIn the keywordsExistence of a Total Order in Every SetAbdelmadjid BoudaoudProblem statement: The axiom of choice, guarantees that all set could be well-ordered, in particular linearly ordered. But the proof in this case was not effective, that was to say, non constructive. It was natural to ask if there was mathematics in which we could given a more constructive proof. Approach: We work in the Nelson’s IST which was an … …Journal of Mathematics and Statistics, Vol. 8, Issue 2 · 16 Mar 2012 · 7,310 accessesView PDFCite