Geodesic
Categoricity spectra of computable structures
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University, Tome 157 (2018), pp. 42-58

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The categoricity spectrum of a computable structure $S$ is the set of all Turing degrees capable of computing isomorphisms among arbitrary computable presentations of $S$. The degree of categoricity of $S$ is the least degree in the categoricity spectrum of $S$. The paper gives a survey of results on categoricity spectra and degrees of categoricity for computable structures. We focus on the results about degrees of categoricity for linear orders and Boolean algebras. We build a new series of examples of degrees of categoricity for linear orders.
Keywords: computable categoricity, categoricity spectrum, degree of categoricity, computable structure, linear order, Boolean algebra, decidable categoricity, autostability, autostability relative to strong constructivizations, index set. 
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     author = {N. A. Bazhenov},
     title = {Categoricity spectra of computable structures},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {42--58},
     publisher = {mathdoc},
     volume = {157},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_157_a2/}
}
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N. A. Bazhenov. Categoricity spectra of computable structures. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University, Tome 157 (2018), pp. 42-58. http://geodesic.mathdoc.fr/item/INTO_2018_157_a2/