La reconstruction au sens de Ulam de certaines multirelations binaires. (The reconstruction in Ulam's sense of some binary multirelations) (Q1182878)

This note studies binary relations \(R,R'\subseteq E\times E\) which are reconstructions of each other in the sense that for every \(x\in E\) the restrictions of \(R\) and \(R'\) to \(E\backslash\{x\}\) are isomorphic. The property of Ulam reconstructibility, expressed by the fact that a relation is isomorphic to all its reconstructions, does not hold for arbitrary relations. However extending this notion to a family \((R_ i)_{i\in I}\) of relations leads to the result that for finite sets \(E\) of at least 7 elements and families containing at least one linear ordering, Ulam reconstructibility always holds.