On the semilattice of weak orders of a set
A weak order on a set X is a binary relation P that is reflexive, transitive and total in that for x,y\(\in X\), xPy or yPx. Order theoretic and combinatorial properties of the semilattice of weak orders on a set are developed. In the case of a finite set, an order theoretic characterization of this semilattice is obtained. Though it is not specifically mentioned in the paper, it follows from property (F2) on p. 234, that the semilattice of weak orders on a finite set X is isomorphic to the semilattice of chains from \(\emptyset\) to X in the power set of X.
scientific article; zbMATH DE number 3883874
scientific article