Skip to main content
SpringerLink
Log in

On the Ershov Upper Semilattice

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We find some links between Σ-reducibility and T-reducibility. We prove that (1) if a quasirigid model is strongly Σ-definable in a hereditarily finite admissible set over a locally constructivizable B-system, then it is constructivizable; (2) every abelian p-group and every Ershov algebra is locally constructivizable; (3) if an antisymmetric connected model is Σ-definable in a hereditarily finite admissible set over a countable Ershov algebra then it is constructivizable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ershov Yu. L., Definability and Computability [in Russian], Nauchnaya Kniga, Novosibirsk (1996).

    Google Scholar 

  2. Goncharov S. S. and Ershov Yu. L., Constructive Models [in Russian], Nauchnaya Kniga, Novosibirsk (1999).

    Google Scholar 

  3. Goncharov S. S., Countable Boolean Algebras and Decidability [in Russian], Nauchnaya Kniga, Novosibirsk (1996).

    Google Scholar 

  4. Ershov Yu. L., “Σ-Definability in admissible sets,” Dokl. Akad. Nauk SSSR, 285,No. 4, 792-795 (1985).

    Google Scholar 

  5. Goncharov S. S., “Constructivizability of the the Cartesian powers of models,” in: Abstracts: 15 All-Union Algebraic Conference, Krasnoyarsk Univ., Krasnoyarsk, 1979, p. 40.

    Google Scholar 

  6. Khisamiev A. N., “On definability of a model in a hereditarily finite admissible set,” in: Generalized Computability and Definability [in Russian], Novosibirsk, 1998, pp. 15-20. (Vychislitel'nye Sistemy; 161.)

  7. Khisamiev A. N., “Numbering and definability in the hereditary finite superstructure of a model,” Siberian Adv. Math., 7,No. 3, 63-74 (1997).

    Google Scholar 

  8. Khisamiev A. N., “Strong Δ1-definability of a model in an admissible set,” Sibirsk. Mat. Zh., 39,No. 1, 191-200 (1998).

    Google Scholar 

  9. Puzarenko V. G., “Computability over models of decidable theories,” Algebra i Logika, 39,No. 2, 170-197 (2000).

    Google Scholar 

  10. Richter L. J., “Degrees of structures,” J. Symbolic Logic, 46,No. 4, 723-731 (1981).

    Google Scholar 

  11. Fuchs L., Infinite Abelian Groups. Vol. 2 [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  12. Fuchs L., Infinite Abelian Groups. Vol. 1 [Russian translation], Mir, Moscow (1974).

    Google Scholar 

  13. Khisamiev A. N., “The intrinsic enumerability of linear orders,” Algebra i Logika, 39,No. 6, 741-751 (2000).

    Google Scholar 

  14. Romina A. V., “Definability of Boolean algebras in \({\mathbb{H}}{\mathbb{F}}\)-superstructures,” Alge bra i Logika, 39,No. 6, 711-720 (2000).

    Google Scholar 

  15. Goncharov S. S., “Constructivizability of superatomic Boolean algebras,” Algebra i Logika, 12,No. 1, 31-40 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk

    A. N. Khisamiev

Authors
  1. A. N. Khisamiev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khisamiev, A.N. On the Ershov Upper Semilattice. Siberian Mathematical Journal 45, 173–187 (2004). https://doi.org/10.1023/B:SIMJ.0000013023.90154.bb

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:SIMJ.0000013023.90154.bb

Search

Navigation