Forbidden configurations for distributive, modular and semidistributive posets

In this paper, we give characterizations for distributive, modular, semidistributive, semimodular, 0 -distributive and 0 -modular lattices using incomparability relations. We generalize these concepts to posets and call them ź -distributive, ź -modular, ź -semidistributive, L U -semimodular, 0 - ź -distributive and 0 - ź -modular posets and obtain forbidden configurations for these classes with finite length by means of L U -subposets.