Skip to main content

Recursive equivalence: A survey

  • Conference paper
  • First Online:
Proceedings of the Summer School in Logic Leeds, 1967

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 70))

  • 322 Accesses

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

Access this chapter

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

  1. P.H.G. Aczel D. Phil. Thesis, Oxford (1966).

    Google Scholar 

  2. -Paths in Kleene's 0, Archiv für math. Logik und Grundlagenforschung, 10 (1967), 8–12.

    Article  MathSciNet  MATH  Google Scholar 

  3. -& J.N. Crossley, Constructive Order Types, III, Archiv für math. Logik und Grundlagenforschung, 9 (1967), 112–116.

    Article  MathSciNet  MATH  Google Scholar 

  4. J.N. Crossley, Constructive Order Types, I, in Formal Systems and Recursive Functions, Amsterdam (1965), 189–264.

    Google Scholar 

  5. -Constructive Order Types, II, Journal of Symbolic Logic, 31 (1966), 525–538.

    Article  MathSciNet  MATH  Google Scholar 

  6. J.N. Crossley, Constructive Order Types, monograph to be published by North Holland Pub. Co., Amsterdam.

    Google Scholar 

  7. J.N. Crossley, & A. Nerode, Effective Dedekind Types, monograph in preparation.

    Google Scholar 

  8. -, & R.J. Parikh, On Isomorphisms of Recursive Well-orderings (abstract), Journal of Symbolic Logic, 28 (1963), 308. (See correction in [5]).

    Google Scholar 

  9. -& K. Schütte Non-uniqueness at w 2 in Kleene's O, Archiv für math. Logik und Grundlagenforschung, 9 (1967), 95–101.

    Article  MATH  Google Scholar 

  10. J.C.E. Dekker A non-constructive extension of the number system (abstracts), Journal of Symbolic Logic, 20 (1955) 204–205.

    Google Scholar 

  11. J.C.E. Dekker Regressive Isols, in Sets, Models and Recursion Theory, Amsterdam (1967), 272–296.

    Google Scholar 

  12. -& J. Myhill Recursive Equivalence Types, University of California Publications in Mathematics (new series) 3 (1960), 67–214.

    MathSciNet  MATH  Google Scholar 

  13. E. Ellentuck The Universal Properties of Dedekind Finite Cardinals, Annals of Mathematics, 82 (1965), 225–248.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Feferman Systems of Predicative Analysis, II: Representations of Ordinals, to appear in Journal of Symbolic Logic.

    Google Scholar 

  15. R.M. Friedberg The Uniqueness of finite division for Recursive Equivalence Types, Math. Zeitschrift, 75 (1961) 3–7.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. G. Hamilton An Unsolved Problem in the theory of Constructive Order Types, to appear in Journal of Symbolic Logic.

    Google Scholar 

  17. S. C. Kleene On the forms of Predicates in the theory of Constructive Ordinals (second paper), American Journal of Mathematics, 77 (1955), 405–428.

    Article  MathSciNet  MATH  Google Scholar 

  18. G. Kreisel review of [4] to appear in Zentralblatt für Mathematik.

    Google Scholar 

  19. A. Manaster Full Co-ordinals of RETs, submitted to Pacific Journal of Mathematics.

    Google Scholar 

  20. J. Myhill Recursive Equivalence Types and Combinatorial Functions, Bulletin of the American Mathematical Society, 64 (1958), 373–376.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Myhill Recursive Equivalence Types and Combinatorial Functions, Proceedings of the 1960 International Congress in Logic, Methodology and Philosophy of Science, Stanford (1962).

    Google Scholar 

  22. -Ω−Λ in Recursive Function Theory, American Mathematical Society Proceedings of Symposia in Pure Mathematics 5 (1962), 97–104.

    Article  MathSciNet  Google Scholar 

  23. -Elementary Properties of the Group of Isolic Integers, Math. Zeitschrift, 78 (1962), 126–130.

    Article  MathSciNet  MATH  Google Scholar 

  24. A. Nerode Extensions to Isols, Annals of Mathematics, 73 (1961), 362–403.

    Article  MathSciNet  MATH  Google Scholar 

  25. -Additive relations among Recursive Equivalence Types, Mathematische Annalen, 159, 329–343 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  26. -Combinatorial Series and Recursive Equivalence Types, Fundamenta Mathematicae, 58 (1966), 113–141.

    MathSciNet  MATH  Google Scholar 

  27. A.J. Page Ph.D. Thesis, Cambridge (1966)

    Google Scholar 

  28. K. Schütte Predicative Well-orderings, in Formal Systems and Recursive Functions, Amsterdam (1965), 280–303.

    Google Scholar 

  29. A. Tarski Ordinal Algebras, Amsterdam (1956)

    Google Scholar 

  30. O. Veblen Continuous Increasing Functions of Finite and Transfinite Ordinals, Transactions of the American Mathematical Society, 9 (1908), 280–292.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. H. Löb

Rights and permissions

Reprints and permissions

Copyright information

© 1968 Springer-Verlag

About this paper

Cite this paper

Crossley, J.N. (1968). Recursive equivalence: A survey. In: Löb, M.H. (eds) Proceedings of the Summer School in Logic Leeds, 1967. Lecture Notes in Mathematics, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079098

Download citation

  • DOI: https://doi.org/10.1007/BFb0079098

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04240-2

  • Online ISBN: 978-3-540-35886-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics