Lattices of Order-Convex Sets of Forests

Author： Semenova Marina  

Publisher： Springer Publishing Company

ISSN： 0167-8094

Source： Order, Vol.27, Iss.3, 2010-11, pp. : 383-404

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Abstract

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.

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