Computable categoricity versus relative computable categoricity
Rodney G. Downey, Asher M. Kach, Steffen Lempp, Daniel D. Turetsky (2013)
Fundamenta Mathematicae
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We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively Δ⁰₂ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both...