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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.: Year: Volume: Issue: Page: Find

 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 157, Pages 42–58 (Mi into406)

Categoricity spectra of computable structures

N. A. Bazhenovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: 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

 Funding Agency Grant Number Russian Science Foundation 18-11-00028 This work was partially supported by the Russian Science Foundation (project No. 18-11-00028).

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UDC: 510.674, 510.532, 512.56
MSC: 03C57, 03D45

Citation: N. A. Bazhenov, “Categoricity spectra of computable structures”, Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 157, VINITI, Moscow, 2018, 42–58

Citation in format AMSBIB
\Bibitem{Baz18} \by N.~A.~Bazhenov \paper Categoricity spectra of computable structures \inbook Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2018 \vol 157 \pages 42--58 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into406}