Interpretation of graphs in the lattices of dimension three
type: Item
instance of: scholarly article
title: Interpretation of graphs in the lattices of dimension three
zbMATH Open document ID: 0855.03021
DOI: 10.1007/BF02107341
author: K. M. Shegirov
published in: Siberian Mathematical Journal
publication date: 1997-01-29T00:00:00Z
review text: \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.
reviewed by: Martin Weese
Mathematics Subject Classification ID: 03C45
zbMATH DE Number: 923552
zbMATH Keywords: stability
zbMATH Keywords: categoricity
zbMATH Keywords: height
zbMATH Keywords: dimension of a partial ordering
zbMATH Keywords: graph
zbMATH Keywords: lattices
zbMATH Keywords: nonsuperstable stable lattice
MaRDI profile type: Publication
cites work: Q4034799
cites work: Stable geometric lattices
cites work: Partially Ordered Sets
cites work: Superstable graphs
cites work: Stable graphs
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description: scientific article; zbMATH DE number 923552