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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References:

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