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Degrees of categoricity of computable structures. (English) Zbl 1184.03026
Summary: Defining the degree of categoricity of a computable structure \({\mathcal{M}}\) to be the least degree \(\mathbf d\) for which \({\mathcal{M}}\) is \(\mathbf d\)-computably categorical, we investigate which Turing degrees can be realized as degrees of categoricity. We show that, for all \(n\), degrees d.c.e. in and above \(\mathbf 0^{(n)}\) can be so realized, as can the degree \(\mathbf 0^{(\omega)}\).

03C57 Computable structure theory, computable model theory
03C35 Categoricity and completeness of theories
03D28 Other Turing degree structures
Full Text: DOI
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