Avoidable structures. I: Finite ordered sets, semilattices and lattices
If \textbf{A} and \textbf{B} are structures, then \textbf{B} avoids \textbf{A} if \textbf{A} cannot be embedded into \textbf{B}. Two structures are said to be incomparable if each of them avoids the other. Let \(K\) be a class of structures of a given signature and \({\mathbf A}\in K\). Then \textbf{A} is said to be avoidable in \(K\) if there exists an infinite set \(S\) of pairwise incomparable finite structures from \(K\) such that every structure from \(S\) avoids \textbf{A}. In the paper, the authors find all finite unavoidable ordered sets, semilattices and lattices.
scientific article; zbMATH DE number 5652281