Dimension may exceed width (Q1112851)

It is well known that the dimension of a partially ordered set P cannot exceed its width, dim(P)\(\leq w(P)\), if the latter is finite. The authors answer a question of W. T. Trotter jun. by showing that for every infinite cardinal \(\chi\), there is a partially ordered set P having infinite width and no infinite antichains such that \(\dim (P)=| P| =\chi\). Thus, the dimension of a partially ordered set may exceed its width, when the width is infinite.