References
D. Hilbert and P. Bernays, Grundlagen der Mathematik, vol. 2, Berlin, 1939.
S. C. Kleene, Introduction to Metamathematics, New York, Toronto, Amsterdam and Groningen, 1952.
S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals, Amer. J. of Math., vol. 66 (1944), pp. 41–58 and vol. 77 (1955), pp. 405–428.
S. W. Markwald, Zur Theorie der konstruktiven Wohlordnungen, Math. Ann., vol. 127 (1954), pp. 135–149.
J. Shoenfield, The class of recursive functions, Proc. Amer. Math. Soc., vol. 9 (1958), pp. 690–692.
C. Spector, Recursive well-orderings, J. of Symb. Log., vol. 20 (1955), pp. 151–163.
C. Spector, Strongly invariant hierarchies, Abstract, Notices of Amer. Math. Soc., vol. 5 (1958), p. 851.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kreisel, G., Shoenfield, J. & Wang, H. Number theoretic concepts and recursive well-orderings. Arch math Logik 5, 42–64 (1960). https://doi.org/10.1007/BF01977642
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01977642