Geodesic
Lattice-inadmissible incidence structures
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 199-209

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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 J^p_L 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 J^p_L.
Keywords: complete lattices, join-independent and meet-independent sets, incidence structures 
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Machala, Frantisek; Slezák, Vladimír. Lattice-inadmissible incidence structures. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 199-209. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a3/