Advertisement

Recursive equivalence: A survey

  • John N. Crossley
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 70)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P.H.G. Aczel D. Phil. Thesis, Oxford (1966).Google Scholar
  2. [2]
    -Paths in Kleene's 0, Archiv für math. Logik und Grundlagenforschung, 10 (1967), 8–12.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    -& J.N. Crossley, Constructive Order Types, III, Archiv für math. Logik und Grundlagenforschung, 9 (1967), 112–116.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J.N. Crossley, Constructive Order Types, I, in Formal Systems and Recursive Functions, Amsterdam (1965), 189–264.Google Scholar
  5. [5]
    -Constructive Order Types, II, Journal of Symbolic Logic, 31 (1966), 525–538.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    J.N. Crossley, Constructive Order Types, monograph to be published by North Holland Pub. Co., Amsterdam.Google Scholar
  7. [7]
    J.N. Crossley, & A. Nerode, Effective Dedekind Types, monograph in preparation.Google Scholar
  8. [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. [9]
    -& K. Schütte Non-uniqueness at w 2 in Kleene's O, Archiv für math. Logik und Grundlagenforschung, 9 (1967), 95–101.CrossRefzbMATHGoogle Scholar
  10. [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. [11]
    J.C.E. Dekker Regressive Isols, in Sets, Models and Recursion Theory, Amsterdam (1967), 272–296.Google Scholar
  12. [12]
    -& J. Myhill Recursive Equivalence Types, University of California Publications in Mathematics (new series) 3 (1960), 67–214.MathSciNetzbMATHGoogle Scholar
  13. [13]
    E. Ellentuck The Universal Properties of Dedekind Finite Cardinals, Annals of Mathematics, 82 (1965), 225–248.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    S. Feferman Systems of Predicative Analysis, II: Representations of Ordinals, to appear in Journal of Symbolic Logic.Google Scholar
  15. [15]
    R.M. Friedberg The Uniqueness of finite division for Recursive Equivalence Types, Math. Zeitschrift, 75 (1961) 3–7.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    A. G. Hamilton An Unsolved Problem in the theory of Constructive Order Types, to appear in Journal of Symbolic Logic.Google Scholar
  17. [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.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    G. Kreisel review of [4] to appear in Zentralblatt für Mathematik.Google Scholar
  19. [19]
    A. Manaster Full Co-ordinals of RETs, submitted to Pacific Journal of Mathematics.Google Scholar
  20. [20]
    J. Myhill Recursive Equivalence Types and Combinatorial Functions, Bulletin of the American Mathematical Society, 64 (1958), 373–376.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [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. [22]
    -Ω−Λ in Recursive Function Theory, American Mathematical Society Proceedings of Symposia in Pure Mathematics 5 (1962), 97–104.MathSciNetCrossRefGoogle Scholar
  23. [23]
    -Elementary Properties of the Group of Isolic Integers, Math. Zeitschrift, 78 (1962), 126–130.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    A. Nerode Extensions to Isols, Annals of Mathematics, 73 (1961), 362–403.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    -Additive relations among Recursive Equivalence Types, Mathematische Annalen, 159, 329–343 (1965).MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    -Combinatorial Series and Recursive Equivalence Types, Fundamenta Mathematicae, 58 (1966), 113–141.MathSciNetzbMATHGoogle Scholar
  27. [27]
    A.J. Page Ph.D. Thesis, Cambridge (1966)Google Scholar
  28. [28]
    K. Schütte Predicative Well-orderings, in Formal Systems and Recursive Functions, Amsterdam (1965), 280–303.Google Scholar
  29. [29]
    A. Tarski Ordinal Algebras, Amsterdam (1956)Google Scholar
  30. [30]
    O. Veblen Continuous Increasing Functions of Finite and Transfinite Ordinals, Transactions of the American Mathematical Society, 9 (1908), 280–292.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • John N. Crossley
    • 1
  1. 1.All Souls CollegeOxford

Personalised recommendations