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A complete organize on finite subsets of an ordered clique
Let $(A,<)$ breathe an ordered clique. Then I outline an ordering on the clique of finite subsets of $A$ as follows. I say that $Xprec Y$ if and provided that the smallest component of $Xtriangle Y$ (the symmetric dissimilarity) is contained in $X$. An simple, however not utterly trifling, commentary is that $prec$ really defines a complete organize on the household of finite subsets of $A$. My query is whether or not this development is well-known.
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