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Degrees of Autostability for Prime Boolean Algebras

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Algebra and Logic Aims and scope

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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    N. A. Bazhenov

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    N. A. Bazhenov

  3. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    M. I. Marchuk

Authors
  1. N. A. Bazhenov
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  2. M. I. Marchuk
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Correspondence to N. A. Bazhenov.

Additional information

*Supported by RFBR, project No. 16-31-60058 mol_a_dk.

**Supported by RFBR (project No. 14-01-00376) and by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-6848.2016.1).

Translated from Algebra i Logika, Vol. 57, No. 2, pp. 149-174, March-April, 2018.

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Bazhenov, N.A., Marchuk, M.I. Degrees of Autostability for Prime Boolean Algebras. Algebra Logic 57, 98–114 (2018). https://doi.org/10.1007/s10469-018-9483-8

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  • DOI: https://doi.org/10.1007/s10469-018-9483-8

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