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We develop tools for studying dendrites and monotone maps between them by examining the Cantor-Bendixson rank of certain subsets of arcs. Using these tools, we prove that the class of monotonely homogeneous dendrites is precisely the class of dendrites which contain a copy of the Omiljanowski dendrite L 0 , answering a question originally asked by J. J. Charatonik. 2000 Mathematics Subject Classification. Primary 54F50, 54C10, 54F65.doi:10.1216/rmj-2011-41-6-2057 fatcat:7qsun2lpunchxdb2iu6g3yv3oy