Skip to main content

On recursion in \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{E}\)and semi-spector classes

Part of the Lecture Notes in Mathematics book series (LNM,volume 689)

Keywords

  • Order Relation
  • Partial Function
  • Finite Sequence
  • Constant Symbol
  • Inductive Relation

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   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

  • P. Aczel [1972], Stage Comparison theorems and game playing with inductive definitions, unpublished notes.

    Google Scholar 

  • K. J. Barwise, R. O. Gandy and Y. N. Moschovakis [1971], The next admissible set, J. Symb. Logic 36 (1971), 108–120.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • R. O. Gandy [1960], Proof of Mostowski's conjecture. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 8 (1960), 571–575.

    MathSciNet  MATH  Google Scholar 

  • T. J. Grilliot [1971], Inductive Definitions and Computability, Trans. Amer. Math. Soc. 158 (1971), 309–317.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • L. A. Harrington, L. M. Kirousis, T. S. Schlipf [1977], A generalized Kleene-Moschovakis theorem, to appear in Proc. of Amer. Math. Soc.

    Google Scholar 

  • A. S. Kechris [1973], The structure of envelopes: a survey of recursion theory in higher types, M.I.T. Logic Seminar notes.

    Google Scholar 

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

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Ph. G. Kolaitis [1977], Recursion in a quantifier vs. elementary induction, to appear in J. Symb. Logic.

    Google Scholar 

  • Ph. G. Kolaitis [1978], Doctoral Dissertation, University of California, Los Angeles.

    Google Scholar 

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

    Google Scholar 

  • Y. N. Moschovakis [1969a], Abstract first order computability II, Trans. Amer. Math. Soc. 138 (1969), 464–504.

    MathSciNet  MATH  Google Scholar 

  • Y. N. Moschovakis [1969b], Abstract computability and invariant definability, J. Symb. Logic 34 (1969), 605–633.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Y. N. Moschovakis [1970], The Suslin-Kleene theorem for countable structures, Duke Math. J. 37 (1970), 341–352.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Y. N. Moschovakis [1974a], Structural characterizations of classes of relations, J. E. Fenstad-P. G. Hinman (eds.), Generalized Recursion Theory, North Holland (1974), 53–79.

    Google Scholar 

  • Y. N. Moschovakis [1974b], On nonmonotone inductive definability, Fundamenta Mathematicae 82 (1974), 39–83.

    MathSciNet  MATH  Google Scholar 

  • Y. N. Moschovakis [1976], On the basic notions in the theory of induction, to appear in Proc. Fifth International Congress of Logic, Methodology and Philosophy of Science.

    Google Scholar 

  • W. Richter [1971], Recursively Mahlo ordinals and inductive definitions, R. O. Gandy-C. E. M. Yates (eds.), Logic Colloquium 69, North Holland (1971), 273–288.

    Google Scholar 

  • W. Richter and P. Aczel [1974], Inductive definitions and reflecting properties of admissible ordinals, Generalized Recursion Theory, J. E. Fenstad-P. G. Hinman (eds.), North Holland (1974), 301–381.

    Google Scholar 

  • C. Spector [1960], Hyperarithmetical quantifiers, Fundamenta Mathematicae 48 (1960), 313–320.

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Kolaitis, P.G. (1978). On recursion in \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{E}\)and semi-spector classes. In: Kechris, A.S., Moschovakis, Y.N. (eds) Cabal Seminar 76–77. Lecture Notes in Mathematics, vol 689. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069302

Download citation

  • DOI: https://doi.org/10.1007/BFb0069302

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09086-1

  • Online ISBN: 978-3-540-35626-4

  • eBook Packages: Springer Book Archive