Lattices of Order-Convex Sets of Forests

• DOI: 10.1007/s11083-009-9119-7
• Publication Date: 2009-07-15T08:29:14Z
• Authors: Marina Semenova; Anna Zamojska-Dzi...
• Keywords: 0102 computer and information sciences; 01 natural sciences

We give a characterization of the class $\mathbf{Co}(\mathcal{F})$ [ $\mathrm{\mathbf{Co}}(\mathcal{F}_n)$ , n < ω, respectively] of lattices isomorphic to convexity lattices of posets which are forests [forests of length at most n, respectively], as well as of the class $\mathbf{Co}(\mathcal{L})$ of lattices isomorphic to convexity lattices of linearly ordered posets. This characterization yields that the class of finite members from $\mathbf{Co}(\mathcal{F})$ [from $\mathbf{Co}(\mathcal{F}_n)$ , n < ω, or from $\mathbf{Co}(\mathcal{L})$ ] is finitely axiomatizable within the class of finite lattices.