Categoricity Spectra of Computable Structures

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 . This paper is a survey of results on catego...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 256; no. 1; pp. 34 - 50
Main Author Bazhenov, N. A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2021
Springer
Springer Nature B.V
Subjects
Algebra
Boolean algebra
Isomorphism
Mathematics
Mathematics and Statistics
Surveys
linear order
index set
computable categoricity
categoricity spectrum
Boolean algebra
autostability
autostability relative to strong constructivizations
degree of categoricity
03C57
03D45
computable structure
decidable categoricity
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-021-05419-x

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Summary: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 . This paper is 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 construct a new series of examples of degrees of categoricity for linear orders.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05419-x