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Algebra and Logic

, Volume 57, Issue 2, pp 98–114 | Cite as

Degrees of Autostability for Prime Boolean Algebras

  • N. A. Bazhenov
  • M. I. Marchuk
Article
  • 13 Downloads

We look at the concept of algorithmic complexity of isomorphisms between computable copies of Boolean algebras. Degrees of autostability are found for all prime Boolean algebras. It is shown that for any ordinals α and β with the condition 0 ≤ α ≤ β ≤ ω, there is a decidable model for which 0(α) is a degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability. It is proved that for any nonzero ordinal β ≤ ω, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while 0(β) is a degree of autostability.

Keywords

autostability spectrum degree of autostability Boolean algebra autostability prime model computable model computable categoricity categoricity spectrum degree of categoricity decidable model autostability relative to strong constructivizations 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

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

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