“…In particular, if B ∩ ↓A = ∅, it can be split into two subsets (A and B) so that every element of L \ C is above A or below B. This fact has a direct connection to the splitting property of posets (see [1,2,6,9,10,11,13]). Indeed, in [14] it is proved that finite maximal antichains in the poset arising from the category C of relational structures with one relation contain no elements of ↓wld( C) \ wld( C).…”