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Algebra and Logic

, Volume 51, Issue 5, pp 384–403 | Cite as

Constructivizability of the boolean algebra \( \mathfrak{B}\left( \omega \right) \) with a distinguished automorphism

  • N. A. Bazhenov
  • R. R. Tukhbatullina
Article

A constructivizability criterion for the Boolean algebra \( \mathfrak{B}\left( \omega \right) \) with a distinguished automorphism is given. As a consequence of the criterion, combined with a result due to I. Sh. Kalimullin, B. M. Khoussainov, and A. G. Melnikov, we construct a Boolean algebra with a distinguished automorphism whose degree spectrum contains every nonzero Turing \( \Delta_2^0 \) -degree but does not contain 0.

Keywords

Boolean algebra with distinguished automorphism constructivizability degree spectra of structures 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Novosibirsk State UniversityNovosibirskRussia
  2. 2.CERGE–EI, a joint workplace of Charles Univ. and Economics Inst. Acad. Sci. Czech RepubPragueCzech Republic

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