Abstract
A tower in an ordered set (X, ⩽) is defined to be a subsetS ofX which has the property that for everysεS there is a maximal chainC in {xεX|x⩽s} which is wholly contained inS. An ordered set (X, ⩽) is called tower-homogeneous if every order isomorphism between towers in (X, ⩽) can be extended to an automorphism of (X, ⩽). It is shown that a finite ordered set is tower-homogeneous if and only if it can be built up from singletons stepwise by constructions of three different types.
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Communicated by I. Rival
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Behrendt, G. Homogeneity in finite ordered sets. Order 10, 65–75 (1993). https://doi.org/10.1007/BF01108709
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DOI: https://doi.org/10.1007/BF01108709