Sub-representation of posets (Q2782214)

Let \(P\) be a poset and \(\hookrightarrow\) a preorder on the set \(\mathcal P(P)\) of all subsets of \(P\) given by embeddability. Let \(\overline{\mathcal P}(P)\) be the associated order. One has an isotone surjection \(i:\mathcal P(P)\to\overline{\mathcal P}(P)\) from \((\mathcal P(P),\subseteq)\) sending a subset to its equivalence class given by embeddability. The authors define sub-representable posets and their definition exactly says that \(i\) can be split by an isotone map \(\overline{\mathcal P}(P)\to \mathcal P(P)\). Then they give a complete characterization of sub-representable posets.NEWLINENEWLINEFor the entire collection see [Zbl 0983.00046].