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Categoricity in hyperarithmetical degrees. (English) Zbl 0617.03016
We obtain, under certain assumptions, necessary and sufficient conditions for a recursive structure to be \(\Delta^ 0_{\alpha}\)-categorical. This is done using the author’s \(\alpha\)-systems to construct suitable \(\Delta^ 0_{\alpha +1}\) functions. We show how these results may be applied, for example, to superatomic Boolean algebras.

MSC:
03C57 Computable structure theory, computable model theory
03C35 Categoricity and completeness of theories
03D30 Other degrees and reducibilities in computability and recursion theory
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