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We prove that for every computable limit ordinal α there exists a computable structure A which is ∆ 0 α -categorical and α is smallest such, but nonetheless for every isomorphic computable copy B of A there exists a β < α such that A ∼ = ∆ 0 β B. This answers a question raised by Kalimullin in personal communication with the third author.doi:10.1090/proc/13954 fatcat:zzqwuhsk7ngk5i56slt6yopf54