Skip to main content

On Rogers Semilattices

  • Conference paper
  • 1030 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3959))

Abstract

Rogers semilattices of computable numberings for the families in the hierarchy of Ershov are compared with those for the families in the arithmetical hierarchy.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Handbook on Recursive Mathematics. Recursive model theory, vol. 1. Elsevier, Amsterdam (1998)

    Google Scholar 

  2. Handbook on Recursive Mathematics. Recursive Algebra, Analysis and Combinatorics, vol. 2. Elsevier, Amsterdam (1998)

    Google Scholar 

  3. Ershov, Y.L., Goncharov, S.S.: Constructive models. Plenum Press Corp., New- York (1999)

    MATH  Google Scholar 

  4. Goncharov, S.S., Sorbi, A.: Generalized computable numberings and non-trivial Rogers semilattices. Algebra and Logic 36(4), 359–369 (1997)

    Article  MathSciNet  Google Scholar 

  5. Ershov.Y.L.: Theory of Numberings. Nauka, Moscow (1977) (Russian)

    Google Scholar 

  6. Badaev, S.A., Goncharov, S.S.: Theory of numberings: open problems. In: Cholak, P., Lempp, S., Lerman, M., Shore, R. (eds.) Computability Theory and its Applications, vol. 257, pp. 23–38. Contemporary Mathematics, American Mathematical Society, Providence (2000)

    Google Scholar 

  7. Badaev, S., Goncharov, S., Podzorov, S., Sorbi, A.: Algebraic properties of Rogers semilattices of arithmetical numberings. In: Cooper, S.B., Goncharov, S. (eds.) Computability and Models, pp. 45–77. Kluwer Academic/Plenum Publishers, New York (2003)

    Google Scholar 

  8. Khutoretsky, A.B.: On the cardinality of the upper semilattice of computable enumerations. Algebra and Logic 10(5), 348–352 (1971)

    Article  Google Scholar 

  9. Selivanov, V.L.: Two theorems on computable enumerations. Algebra and Logic 15(4), 297–306 (1976)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Badaev, S. (2006). On Rogers Semilattices. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_66

Download citation

  • DOI: https://doi.org/10.1007/11750321_66

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34021-8

  • Online ISBN: 978-3-540-34022-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics