Categorical linearly ordered structures.

We prove that for every computable limit ordinal α there exists a computable linear ordering A which is Δα0-categorical and α is smallest such, but nonetheless for every isomorphic computable copy B of A there exists a β<α such that A≅Δβ0B. 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.