Coding in the automorphism group of a computably categorical structure

Journal of Mathematical Logic 20 (3):2050016 (2020)
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Abstract

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, Kalimullin and Yamaleev. Using the same techniques, we construct a computably categorical structure of non-computable Scott rank.

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10.1142/s0219061320500166

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Degrees That Are Not Degrees of Categoricity.Bernard Anderson & Barbara Csima - 2016 - Notre Dame Journal of Formal Logic 57 (3):389-398.
Categoricity in hyperarithmetical degrees.C. J. Ash - 1987 - Annals of Pure and Applied Logic 34 (1):1-14.

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