Pseudo-similar points in ordered sets

Two points l and h in an ordered set P are called pseudo-similar iff P?{l} is isomorphic to P?{h} and there is no automorphism of P that maps l to h. This paper provides a characterization of ordered sets with at least two pseudo-similar points. Special attention is given to ordered sets with pseudo-similar points l and h so that one of the points is minimal and the other is maximal. These sets will play a key role in the reconstruction of the rank of the removed element in a non-extremal card.