Algebra and Logic

, Volume 44, Issue 3, pp 143–147 | Cite as

Elementary Theories for Rogers Semilattices

  • S. A. Badaev
  • S. S. Goncharov
  • A. Sorbi
Article

Abstract

It is proved that for every level of the arithmetic hierarchy, there exist infinitely many families of sets with pairwise non-elementarily equivalent Rogers semilattices.

Keywords

arithmetic hierarchy Rogers semilattice elementary theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    V. V. V’jugin, “On some examples of upper semilattice of computable numerations,” Algebra Logika, 12, No.5, 512–529 (1973).Google Scholar
  2. 2.
    S. S. Goncharov and A. Sorbi, “Generalized computable numerations and nontrivial Rogers semilattices,” Algebra Logika, 36, No.6, 621–641 (1997).Google Scholar
  3. 3.
    S. A. Badaev and S. S. Goncharov, “Rogers semilattices of families of arithmetic sets,” Algebra Logika, 40, No.5, 507–522 (2001).Google Scholar
  4. 4.
    S. A. Badaev, S. S. Goncharov, and A. Sorbi, “Completeness and universality of arithmetical numberings,” in Computability and Models, S. B. Cooper and S. S. Goncharov (eds.), Kluwer Academic/Plenum Publishers, New York (2003), pp. 11–44.Google Scholar
  5. 5.
    S. A. Badaev, S. S. Goncharov, S. Yu. Podzorov, and A. Sorbi, “Algebraic properties of Rogers semilattices of arithmetical numberings,” in Computability and Models, S. B. Cooper and S. S. Goncharov (eds.), Kluwer Academic/Plenum Publishers, New York (2003), pp. 45–77.Google Scholar
  6. 6.
    S. A. Badaev, S. S. Goncharov, and A. Sorbi, “Isomorphism types and theories of Rogers semilattices of arithmetical numberings,” in Computability and Models, S. B. Cooper and S. S. Goncharov (eds.), Kluwer Academic/Plenum Publishers, New York (2003), pp. 79–91.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. A. Badaev
    • 1
  • S. S. Goncharov
    • 2
  • A. Sorbi
    • 3
  1. 1.KazSUAlmatyKazakhstan
  2. 2.Institute of Mathematics SB RASNovosibirskRussia
  3. 3.Dip. di Scienze Matematiche ed Informatiche “Roberto Magari”SienaItaly

Personalised recommendations