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A Note on Effective Categoricity for Linear Orderings

  • Nikolay Bazhenov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)

Abstract

We study effective categoricity for linear orderings. For a computable structure \(\mathcal {S}\), the degree of categoricity of \(\mathcal {S}\) is the least Turing degree which is capable of computing isomorphisms among arbitrary computable copies of \(\mathcal {S}\).

We build new examples of degrees of categoricity for linear orderings. We show that for an infinite computable ordinal \(\alpha \), every Turing degree c.e. in and above \(\mathbf {0}^{(2\alpha + 2)}\) is the degree of categoricity for some linear ordering. We obtain similar results for linearly ordered abelian groups and decidable linear orderings.

Keywords

Linear ordering Computable categoricity Computable structure Categoricity spectrum Degree of categoricity Autostability spectrum Ordered abelian group Decidable structure Autostability relative to strong constructivizations 

Notes

Acknowledgements

The author is grateful to Sergey Goncharov for fruitful discussions on the subject. The reported study was funded by RFBR, according to the research project No. 16-31-60058 mol_a_dk.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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