Abstract
It is proved that if we replace an autonomous subset of a finite proper trapezoid ordered set with a proper trapezoid ordered set, then we obtain a proper trapezoid ordered set provided the autonomous subset is not an antichain, and analogously in the k-dimensional case. As corollaries we obtain that being a proper trapezoid ordered set is a comparability invariant, more generally, proper interval dimension is a comparability invariant.
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Niederle, J. Being a Proper Trapezoid Ordered Set Is a Comparability Invariant. Order 17, 301–308 (2000). https://doi.org/10.1023/A:1026717230082
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DOI: https://doi.org/10.1023/A:1026717230082