Avoidable structures. I: Finite ordered sets, semilattices and lattices
type: Item
instance of: scholarly article
title: Avoidable structures. I: Finite ordered sets, semilattices and lattices
zbMATH Open document ID: 1208.08001
author: Ralph McKenzie
author: W. Dziobiak
author: Jaroslav Ježek
published in: Algebra Universalis
publication date: 2010-01-04T00:00:00Z
review text: 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.
reviewed by: Jiří Rachůnek
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 5652281
zbMATH Keywords: avoidable structures
zbMATH Keywords: incomparable structures
zbMATH Keywords: ordered sets
zbMATH Keywords: semilattices
zbMATH Keywords: lattices
MaRDI profile type: Publication
full work available at URL: s00012-009-2097-1
OpenAlex ID: W2024133217
DOI: 10.1007/S00012-009-2097-1
description: scientific article; zbMATH DE number 5652281