# Finite sholander trees, trees, and their betweennesses

We provide a proof of a claim made by Sholander (Trees, lattices, order, and betweenness, {\it Proc. Amer. Math. Soc.} {\bf 3}, 369-381 (1952)) concerning the representability of collections of so-called segments by trees. Furthermore, we strengthen Burigana's axiomatic characterization of so-called betweennesses induced by trees (Tree representations of betweenness relations defined by intersection and inclusion, {\it Mathematics and Social Sciences} {\bf 185}, 5-36 (2009)) and provide a short proof.

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Rautenbach, Dieter / Schäfer, Philipp Matthias: Finite sholander trees, trees, and their betweennesses. 2009.

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