Email this article Degrees of Autostability Relative to Strong Constructivizations for Boolean Algebras
- Authors: Bazhenov N.A.1,2,3
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Kazan (Volga Region) Federal University
- Issue: Vol 55, No 2 (2016)
- Pages: 87-102
- Section: Article
- URL: https://journals.rcsi.science/0002-5232/article/view/233976
- DOI: https://doi.org/10.1007/s10469-016-9381-x
- ID: 233976
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Abstract
It is proved that for every computable ordinal α, the Turing degree 0(α) is a degree of autostability of some computable Boolean algebra and is also a degree of autostability relative to strong constructivizations for some decidable Boolean algebra. It is shown that a Harrison Boolean algebra has no degree of autostability relative to strong constructivizations. It is stated that the index set of decidable Boolean algebras having degree of autostability relative to strong constuctivizations is ∏11-complete.
About the authors
N. A. Bazhenov
Sobolev Institute of Mathematics; Novosibirsk State University; Kazan (Volga Region) Federal University
Author for correspondence.
Email: bazhenov@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090; ul. Kremlevskaya 18, Kazan, 420008
