Representation of partially ordered sets

It is well known [1] that any distributive poset (short for partially ordered set) has an isomorphic representation as a poset (Q, (–) such that the supremum and the infimum of any finite setF ofp correspond, respectively, to the union and intersection of the images of the elements ofF. Here necessary and sufficient conditions are given for similar isomorphic representation of a poset where however the supremum and infimum of also infinite subsetsI correspond to the union and intersection of images of elements ofI.Presented by R. Freese.