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arXiv · 1111.1390

On extension of partial orders to total preorders with prescribed symmetric part

Dmitry V. Akopian·Valentin V. Gorokhovik
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Abstract

For a partial order $\preceq$ on a set X and an equivalency relation S defined on the same set X we derive a necessary and sufficient condition for the existence of such a total preorder on X whose asymmetric part contains the asymmetric part of the given partial order $\preceq$ and whose symmetric part coincides with the given equivalence relation S. This result generalizes the classical Szpilrajn theorem on extension of a partial order to a perfect (linear) order.

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Dmitry V. Akopian, Valentin V. Gorokhovik. 2011-11-06. On extension of partial orders to total preorders with prescribed symmetric part. https://arxiv.org/abs/1111.1390

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