Abstract
We study the index sets of the class of d-decidable structures and of the class of d-decidable countably categorical structures, where d is an arbitrary arithmetical Turing degree. It is proved that the first of them is m-complete ∑30, d, and the second is m-complete ∑30, d\∑30, d in the universal computable numbering of computable structures for the language with one binary predicate.
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