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We characterize lattices that are isomorphic to the lattices of convex subsets of partially ordered sets of finite length. We also describe the class of lattices that are isomorphic to the lattices of convex subsets of n-ary trees for any integer n > 1. Bibliography:10 titles., UDC 512.56 + 512.57 + 514.146.01 The lattices of convex subsets of posets are an expressive example of convex geometries (cf. [1] and [2]). These lattices were studied by many [...]