A nonstandard proof for Szpilrajn's theorem

Abstract

Recall that Szpilrajn (1930) ([4], [5]) states that on a given set, any partial order can be extended to a total order on the same set. In this work we give, in the context of the IST theory ([2],[3],[6]), a more constructive proof for this theorem. In addition, we benefit of the tools used to give some other results.

arXiv commentInternational Conference in Mathematics 2012, Mar 2012, Al - Ain (United Arab Emirates University ), United Arab Emirates. Proceedings of the International Conference in Mathematics 2012, 2016, Proceedings of the International Conference in Mathematics 2012