Lattice-inadmissible incidence structures

Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure ${\displaystyle J^p\_\left\{L\right\}}$ of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure ${\displaystyle J^p\_\left\{L\right\}}$.