Skip to main content

Model theoretic characterizations in generalized recursion theory

  • 297 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 859)

Keywords

  • Partial Function
  • Finite Sequence
  • High Type
  • Small Model
  • Abstract Structure

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • A. Grzegorczyk, A. Mostowski and C. Ryll-Nardzewski [1958], The classical and the ω-complete arithmetic, Journal of Symbolic Logic 23 (1958), 188–206.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • A. S. Kechris and Y. N. Moschovakis [1977], Recursion in higher types, J. Barwise (ed.), Handbook of Mathematical Logic, 681–737, North-Holland (1977).

    Google Scholar 

  • S. C. Kleene [1959a], Recursive functionals and quantifiers of finite type I, Trans. Amer. Math. Soc. 91 (1959), 1–52.

    MathSciNet  MATH  Google Scholar 

  • S. C. Kleene [1959b], Quantification of number theoretic functions, Compositio Math. 14 (1959), 23–40.

    MathSciNet  MATH  Google Scholar 

  • Ph. G. Kolaitis [1978], On recursion in E and semi-Spector classes, A. S. Kechris-Y. N. Moschovakis (eds.), Cabal Seminar 76–77, 209–243, Lecture Notes in Mathematics 689, Springer-Verlag (1978).

    Google Scholar 

  • Ph. G. Kolaitis [1979], Recursion in a quantifier vs. elementary induction, Journal of Symbolic Logic 44 (1979), 235–259.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • G. Kreisel [1961], Set theoretic problems suggested by the notion of potential totality, Infinitistic Methods, 103–140, Pergamon (1961).

    Google Scholar 

  • G. Kreisel [1965], The Axiom of choice and the class of hyperarithmetic functions, Indagationes Mathematicae 24 (1962), 307–319.

    MathSciNet  MATH  Google Scholar 

  • D. B. MacQueen [1972], Post's problem for recursion in higher types, Ph.D. Thesis, Massachusetts Institute of Technology (1972).

    Google Scholar 

  • Y. N. Moschovakis [1967], Hyperanalytic predicates, Trans. Amer. Math. Soc. 129 (1967), 249–282.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Y. N. Moschovakis [1969a], Abstract first order computability I, Trans. Amer. Math. Soc. 138 (1969), 427–464.

    MathSciNet  MATH  Google Scholar 

  • Y. N. Moschovakis [1969b], Abstract first order computability II, Trans. Amer. Math. Soc. 138 (1969), 465–504.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Y. N. Moschovakis [1969c], Abstract computability and invariant definability, Journal of Symbolic Logic 34 (1969), 605–633.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Y. N. Moschovakis [EIAS], Elementary Induction on Abstract Structures, North Holland (1974).

    Google Scholar 

  • Y. N. Moschovakis [1977], On the basic notions in the theory of induction, Butts and Hintikka (eds.), Logic, Foundations of Mathematics and Computability Theory, 207–236, Reidel (1977).

    Google Scholar 

  • D. Normann [1978], Set Recursion, J. E. Fendstad, R. O. Gandy, G. E. Sacks (eds.), Generalized recursion theory II, 303–320, North Holland (1978).

    Google Scholar 

  • C. Spector [1961], Inductively defined sets of natural numbers, Infinitistic methods, 97–102, Pergamon (1961).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Kolaitis, P.G. (1981). Model theoretic characterizations in generalized recursion theory. In: Lerman, M., Schmerl, J.H., Soare, R.I. (eds) Logic Year 1979–80. Lecture Notes in Mathematics, vol 859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090943

Download citation

  • DOI: https://doi.org/10.1007/BFb0090943

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10708-8

  • Online ISBN: 978-3-540-38673-5

  • eBook Packages: Springer Book Archive