Interpretation of graphs in the lattices of dimension three
\textit{K. W. Smith} [``Stability and categoricity of lattices'', Can. J. Math. 33, 1380-1419 (1981; Zbl 0474.03012)] showed the superstability of lattices of height 4 and dimension 2 (where the dimension of a partial ordering \((A, <)\) is the least cardinal \(\kappa\) such that \(<\) is the intersection of \(\kappa\) linear orderings on \(A\)). Here the author solves a question posed by Smith. He shows that an arbitrary graph can be interpreted in the class of lattices of height 4 and dimension 3. This implies that there exists a nonsuperstable stable lattice of height 4 and dimension 3.
scientific article; zbMATH DE number 923552