Mathematical Logic Quarterly 49 (6):603 (2003)

Abstract
We investigate the computational complexity the class of Γ-categorical computable structures. We show that hyperarithmetic categoricity is Π11-complete, while computable categoricity is Π04-hard
Keywords Computable structure  categorical structure  Scott family  hyperarithmetic categoricity
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DOI 10.1002/malq.200310066
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Computably Isometric Spaces.Alexander G. Melnikov - 2013 - Journal of Symbolic Logic 78 (4):1055-1085.
Scott Sentences for Certain Groups.Julia F. Knight & Vikram Saraph - 2018 - Archive for Mathematical Logic 57 (3-4):453-472.

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