  Using new techniques for controlling the categoricity spectrum of a
structure, we construct a structure with degree of categoricity but infinite
spectral dimension, answering a question of Bazhenov, Kalimulin and Yamaleev.
Using the same techniques, we construct a computably categorical structure of
non-computable Scott rank, and a structure of computable dimension 2 such that
there is no hyperarithmetic isomorphism between the two copies.

Logic