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Algebra Logika, 2018, Volume 57, Number 2, Pages 149–174 (Mi al841)  

Degrees of autostability for prime Boolean algebras

N. A. Bazhenovab, M. I. Marchukab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: 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 $\alpha$ and $\beta$ with the condition $0\le\alpha\le\beta\le\omega$ there is a decidable model for which $\mathbf0^{(\alpha)}$ is a degree of autostability relative to strong constructivizations, while $\mathbf0^{(\beta)}$ is a degree of autostability. It is proved that for any nonzero ordinal $\beta\le\omega$, there is a decidable model for which there is no degree of autostability relative to strong constructivizations, while $\mathbf0^{(\beta)}$ 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-60058 мол_а_дк
14-01-00376
Ministry of Education and Science of the Russian Federation НШ-6848.2016.1
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).


DOI: https://doi.org/10.17377/alglog.2018.57.202

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English version:
Algebra and Logic, 2018, 57:2, 98–114

Bibliographic databases:

Document Type: Article
UDC: 510.5+512.563
Received: 11.10.2016
Revised: 25.05.2016

Citation: N. A. Bazhenov, M. I. Marchuk, “Degrees of autostability for prime Boolean algebras”, Algebra Logika, 57:2 (2018), 149–174; Algebra and Logic, 57:2 (2018), 98–114

Citation in format AMSBIB
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\pages 149--174
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