Pseudo-similar points in ordered sets

Two points ll and hh in an ordered set PP are called pseudo-similar iff P∖{l}P∖{l} is isomorphic to P∖{h}P∖{h} and there is no automorphism of PP that maps ll to hh. 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 ll and hh 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.