Siberian Mathematical Journal

, Volume 44, Issue 4, pp 561–567 | Cite as

Computable Families of Superatomic Boolean Algebras

  • P. E. Alaev


We describe the families of superatomic Boolean algebras which have a computable numbering. We define the notion of majorizability and establish a criterion that is formulated only on using algorithmic terms and majorizability. We give some examples showing that the condition of majorizability is essential. We also prove some criterion for the existence of a computable numbering for a family of α-atomic algebras (α is a computable ordinal).

computability superatomic Boolean algebra computable structure computable numbering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Goncharov S. S., “Constructivizability of superatomic Boolean algebras,” Algebra i Logika, 12, No. 1, 31–40 (1973).Google Scholar
  2. 2.
    Goncharov S. S., Countable Boolean Algebras and Decidability [in Russian], Nauchnaya Kniga, Novosibirsk (1996).Google Scholar
  3. 3.
    Rogers H., Theory of Recursive Functions and Effective Computability [Russian translation], Mir, Moscow (1972).Google Scholar
  4. 4.
    Ash C. J., “A construction for recursive linear orderings,” J. Symbolic Logic, 56, No. 2, 673–683 (1991).Google Scholar
  5. 5.
    Ash C. J., “Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees,” Trans. Amer. Math. Soc., 298, No. 2, 497–514 (1986).Google Scholar
  6. 6.
    Alaev P. E., “Countable homogeneous Boolean algebras and one metatheorem,” Algebra i Logika (to appear).Google Scholar
  7. 7.
    Ash C. J., “Categoricity in hyperarithmetical degrees,” Ann. Pure Appl. Logic, 34, No. 1, 1–14 (1987).Google Scholar
  8. 8.
    Khisamiev N. G., “A criterion for constructivizability of a direct sum of cyclic p-groups,” Izv. Akad. Nauk Kaz. SSR Ser. Fiz.-Mat., 98, No. 1, 51–55 (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • P. E. Alaev
    • 1
  1. 1.Sobolev Institute of MathematicsNovosibirsk

Personalised recommendations