Skip to main content
SpringerLink
Log in

Model theoretic characterizations in generalized recursion theory

  • Conference paper
  • First Online:
Book cover Logic Year 1979–80

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

  • 336 Accesses

During the preparation of this paper, the author was partially supported by NSF Grant #MCS-8002763.

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

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

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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

  1. Department of Mathematics, The University of Chicago, 60637, Chicago, Illinois

    Phokion G. Kolaitis

Authors
  1. Phokion G. Kolaitis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Manuel Lerman James H. Schmerl Robert I. Soare

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

Publish with us

Policies and ethics

Search

Navigation