Abstract
We survey the current results about degrees of categoricity and the degrees that are low for isomorphism as well as the proof techniques used in the constructions of elements of each of these classes. We conclude with an analysis of these classes, what we may deduce about them given the sorts of proof techniques used in each case, and a discussion of future lines of inquiry.
The author would like to thank the editors of this Festschrift for the invitation to contribute.
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Notes
- 1.
We note with some amusement that the isomorphism condition is actually lower in the arithmetic hierarchy than the others and is therefore not the condition that determines the degree of genericity necessary to force lowness for isomorphism.
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Franklin, J.N.Y. (2017). Strength and Weakness in Computable Structure Theory. In: Day, A., Fellows, M., Greenberg, N., Khoussainov, B., Melnikov, A., Rosamond, F. (eds) Computability and Complexity. Lecture Notes in Computer Science(), vol 10010. Springer, Cham. https://doi.org/10.1007/978-3-319-50062-1_20
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