On weakly cut-stable maps

A mapping f:P→Qf:P→Q between posets P and Q is called weakly cut-stable if f   can be naturally extended to a weakly complete lattice homomorphism (i.e., preserving non-empty meets and joins) f∗:N(P)→N(Q)f∗:N(P)→N(Q) between the corresponding Dedekind–MacNeille completions. These mappings are studied and described by the 1st-order language.