A nonstandard proof for Szpilrajn's theorem

TL;DR

This paper provides a more constructive proof of Szpilrajn's theorem within the IST framework and explores additional related results using the same tools.

Contribution

It introduces a new constructive proof of Szpilrajn's theorem in the IST theory context, expanding the theorem's applications.

Findings

Constructive proof of Szpilrajn's theorem within IST

Extension of partial orders to total orders using new methods

Additional related results derived from the proof tools

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.