Lattices of Order-Convex Sets of Forests |
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| Authors: | Marina Semenova Anna Zamojska-Dzienio |
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| Affiliation: | 1.Institute of Mathematics of the Siberian Branch of Russian Academy of Sciences,Novosibirsk,Russia;2.Faculty of Mathematics and Information Science,Warsaw University of Technology,Warsaw,Poland |
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| Abstract: | We give a characterization of the class Co(F)mathbf{Co}(mathcal{F}) [Co(Fn)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 Co(L)mathbf{Co}(mathcal{L}) of lattices isomorphic to convexity lattices of linearly ordered posets. This characterization yields that the class of finite members from Co(F)mathbf{Co}(mathcal{F}) [from Co(Fn)mathbf{Co}(mathcal{F}_n), n < ω, or from Co(L)mathbf{Co}(mathcal{L})] is finitely axiomatizable within the class of finite lattices. |
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