Skip to main content
SpringerLink
Log in

Index Sets of Computable Structures with Decidable Theories

  • Conference paper
Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

Included in the following conference series:

  • 1261 Accesses

Abstract

The index set of computable structures with decidable theory for some fixed infinite language σ * is m–complete \(\Sigma^{0,\emptyset^{(\omega)}}_2\).

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Calvert, W.: The isomorphism problem for classes of computable fields. Archive for Mathematical Logic 75, 327–336 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Calvert, W.: The isomorphism problem for computable Abelian p-groups of bounded length. Journal of Symbolic Logic 70, 331–345 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Calvert, W., Cummins, D., Knight, J.F., Miller, S.: Comparing classes of finite structures. Algebra and Logic 43, 374–392 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Calvert, W., Harizanov, V., Knight, J.F., Miller, S.: Index sets of computable structures. Algebra and Logic 45, 306–325 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Csima, B.F., Montalbán, A., Shore, R.A.: Boolean algebras, Tarski invariants, and index sets. In the Notre Dame Journal of Formal Logic (to appear)

    Google Scholar 

  6. Dobritsa, V.P.: Complexity of the index set of a constructive model. Algebra and Logic 22, 269–276 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Goncharov, S.S., Knight, J.F.: Computable structure and non-structure theorems. Algebra and Logic (English translation) 41, 351–373 (2002)

    Article  MATH  Google Scholar 

  8. Lempp, S., Slaman, T.: The complexity of the index sets of \(\aleph_{0}\)-categorical theories and of Ehrenfeucht theories, to appear in the Advances in Logic In: Proceedings of the North Texas Logic Conference, Contemporary Mathematics, American Mathematical Society. October 8–10, (2004)

    Google Scholar 

  9. White, W.: On the complexity of categoricity in computable structures. Mathematical Logic Quarterly 49, 603–614 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. White, W.: Characterizations for Computable Structures, PhD dissertation, Cornell University (2000)

    Google Scholar 

  11. Fokina, E.: Index sets of decidable models, Sibirsk. Mat. Zh (To appear)

    Google Scholar 

  12. Goncharov, S., Khoussainov, B.: Complexity of theories of computable categorical models. Algebra Logic 43(6), 365–373 (2004)

    Article  MathSciNet  Google Scholar 

  13. Marker, D.: Non-Σ n -axiomatizable almost strongly minimal theories. J. Symbolic Logic 54, 921–927 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. Fokina, E.: On complexity of categorical theories with computable models. Vestnik NGU 5(2), 78–86 (2005)

    MATH  Google Scholar 

  15. Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill, New York (1967)

    MATH  Google Scholar 

  16. Ash, C.J., Knight, J.F.: Computable Structures and the Hyperarithmetical Hierarchy. In: Studies in Logic and the Foundations of Mathematics, vol. 144, North-Holland Publishing Co., Amsterdam (2000)

    Google Scholar 

  17. Ash, C.J., Knight, J.F.: Pairs of recursive structures. Ann. Pure Appl. Logic 46(3), 211–234 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  18. Goncharov, S., Harizanov, V., Knight, J., McCoy, C., Miller, R., Solomon, R.: Enumerations in computable structure theory. Ann. Pure Appl. Logic 136(3), 219–246 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 4 Acad. Koptyug avenue, 630090 Novosibirsk, Russia

    Ekaterina B. Fokina

Authors
  1. Ekaterina B. Fokina
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fokina, E.B. (2007). Index Sets of Computable Structures with Decidable Theories. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73001-9_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation