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A linear ordering is scattered if it does not contain a copy of the rationals. Hausdorff characterised the class of scattered linear orderings as the least family of linear orderings that includes the class B of well-orderings and reversed well-orderings, and is closed under lexicographic sums with index set in B. More generally, we say that a partial ordering is κ-scattered if it does not contain a copy of any κ-dense linear ordering. We prove analogues of Hausdorff's result for κ-scattereddoi:10.1090/s0002-9947-2012-05466-3 fatcat:nrovdabbobefzbfab4ou35ifi4