Skip to main content
SpringerLink
Log in
Book cover

Conference on Computability in Europe

CiE 2005: New Computational Paradigms pp 209–210Cite as

Computability-Theoretic and Proof-Theoretic Aspects of Vaughtian Model Theory

  • Conference paper

  • 1105 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3526))

Abstract

I will discuss some recent results in the analysis of the computability-theoretic and proof-theoretic content of Vaughtian model theory, that is, the study of special models such as prime, saturated, and homogeneous models, and associated results such as the omitting types theorem. This is a research program dating back to the 1970’s (see [4]), but which has recently picked up steam with the application of finer computability-theoretic tools. Here are two examples.

This is a preview of subscription content, 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

Learn about institutional subscriptions

References

  1. Goncharov, S.S., Nurtazin, A.T.: Constructive models of complete decidable theories. Algebra and Logic 12, 67–77 (1973)

    Article  Google Scholar 

  2. Millar, T.S.: Foundations of recursive model theory. Ann. Math. Logic 13, 45–72 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Millar, T.S.: Omitting types, type spectrum, and decidability. J. Symbolic Logic 48, 171–181 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Harizanov, V.S.: Pure computable model theory. In: Ershov, Y.L., Goncharov, S.S., Nerode, A., Remmel, J.B. (eds.) Handbook of Recursive Mathematics. Stud. Logic Found. Math., pp. 138–139. Elsevier Science, Amsterdam (1998) 3–114

    Google Scholar 

  5. Slaman, T.A.: Relative to any nonrecursive set. Proc. Amer. Math. Soc. 126, 2117–2122 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Wehner, S.: Enumerations, countable structures, and Turing degrees. Proc. Amer. Math. Soc. 126, 2131–2139 (1998)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL, 60637, USA

    Denis R. Hirschfeldt

Authors
  1. Denis R. Hirschfeldt
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  2. Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Benedikt Löwe

  3. Universiteit van Amsterdam,  

    Leen Torenvliet

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hirschfeldt, D.R. (2005). Computability-Theoretic and Proof-Theoretic Aspects of Vaughtian Model Theory. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_25

Download citation

  • DOI: https://doi.org/10.1007/11494645_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26179-7

  • Online ISBN: 978-3-540-32266-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation