## 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 $$\mathbf 0^{(\omega)}$$.

### MSC:

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

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