Skip to main content
SpringerLink
Log in

A class of almost c-simple rings

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We construct a family of almost c-simple rings whose hereditarily finite extension admits universal Σ-functions.

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, Consultants Bureau, New York and London (1996).

    Google Scholar 

  2. Goncharov S. S. and Sviridenko D. I., “Mathematical foundations of semantic programming,” Dokl. Akad. Nauk SSSR, 289, No. 6, 1324–1328 (1986).

    MathSciNet  Google Scholar 

  3. Ershov Yu. L., Goncharov S. S., and Sviridenko D. I., “Semantic programming. Information processing,” in: Proc. IFIP 10th World Comput. Congress. Vol. 10, Elsevier Sci., Dublin, 1986, pp. 1093–1100.

    Google Scholar 

  4. Rudnev V. A., “A universal recursive function on admissible sets,” Algebra and Logic, 25, No. 4, 267–273 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  5. Morozov A. S. and Puzarenko V. G., “Σ-subsets of natural numbers,” Algebra and Logic, 43, No. 3, 162–178 (2004).

    Article  MathSciNet  Google Scholar 

  6. Kalimullin I. Sh. and Puzarenko V. G., “Computable principles on admissible sets,” Siberian Adv. in Math., 15, No. 4, 1–33 (2005).

    MathSciNet  Google Scholar 

  7. Puzarenko V. G., “Computability in special models,” Siberian Math. J., 46, No. 1, 148–165 (2005).

    Article  MathSciNet  Google Scholar 

  8. Aleksandrova S. A., “The uniformization problem for Σ-predicates in a hereditarily finite list superstructure over the real exponential field,” Algebra and Logic, 53, No. 1, 1–8 (2014).

    Article  MathSciNet  Google Scholar 

  9. Korovina M. V., “On a universal recursive function and abstract machines on reals with list superstructure,” in: Structural Algorithmic Properties of Computability (Vychisl. Sistemy; No. 156) [in Russian], Novosibirsk, 1996, pp. 24–43.

    Google Scholar 

  10. Stukachev A. I., “The uniformization theorem in hereditary finite superstructures,” in: Generalized Computability and Definability (Vychisl. Sistemy; No. 161) [in Russian], Izdat. IM SO RAN, Novosibirsk, 1998, 161, pp. 3–14.

    MATH  MathSciNet  Google Scholar 

  11. Khisamiev A. N., “On Σ-subsets of naturals over abelian groups,” Siberian Math. J., 47, No. 3, 574–583 (2006).

    Article  MathSciNet  Google Scholar 

  12. Khisamiev A. N., “Σ-Bounded algebraic systems and universal functions. I,” Siberian Math. J., 51, No. 1, 178–192 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  13. Khisamiev A. N., “Σ-Bounded algebraic systems and universal functions. II,” Siberian Math. J., 51, No. 3, 537–551 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  14. Khisamiev A. N., “On a universal Σ-function over a tree,” Siberian Math. J., 53, No. 3, 551–553 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  15. Khisamiev A. N., “Σ-Uniform structures and Σ-functions. I,” Algebra and Logic, 50, No. 5, 447–465 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  16. Khisamiev A. N., “Σ-Uniform structures and Σ-functions. II,” Algebra and Logic, 51, No. 1, 89–102 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  17. Ershov Yu. L., Puzarenko V. G., and Stukachev A. I., “HF-Computability,” in: Computability in Context: Computation and Logic in the Real World, S. B. Cooper and A. Sorbi (Eds.), Imperial College Press/World Sci., London, 2011, pp. 169–242.

    Chapter  Google Scholar 

  18. Khisamiev A. N., “Universal functions and almost c-simple models,” Siberian Math. J., 56, No. 3, 526–540 (2015).

    Article  Google Scholar 

  19. van der Waerden B. L., Algebra [Russian translation], Lan’, St. Petersburg (2004).

    Google Scholar 

  20. Ershov Yu. L., Multi-Valued Fields, Kluwer Academic/Consultants Bureau, New York (2001).

    Book  Google Scholar 

  21. Chang C. C. and Keisler H. J., Model Theory, North-Holland, Amsterdam and London (1973).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. N. Khisamiev

  2. Novosibirsk State University, Novosibirsk, Russia

    A. N. Khisamiev

Authors
  1. A. N. Khisamiev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Khisamiev.

Additional information

Original Russian Text Copyright © 2015 Khisamiev A.N.

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 6, pp. 1416–1425, November–December, 2015; DOI: 10.17377/smzh.2015.56.617.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khisamiev, A.N. A class of almost c-simple rings. Sib Math J 56, 1133–1141 (2015). https://doi.org/10.1134/S0037446615060178

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446615060178

Keywords

Search

Navigation