Browsing by Author "Ng, Keng Meng"

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    Categorical Linearly Ordered Structures
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2018) Downey, Rod; Melnikov, Alexander; Ng, Keng Meng
    We prove that for every computable limit ordinal α there exists a computable linear ordering A which is Δ^(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≅Δ0βB. This answers a question left open in the earlier work of Downey, Igusa, and Melnikov. We also show that such examples can be found among ordered abelian groups and real-closed fields.