A classification of the ordinal recursive functions

Davis, M., Computability and Unsolvability, McGraw-Hill (1958).

Gödel, K., Über eine bisher noch nicht benützte Erweiterung des Finiten Standpunktes, Dialectica12 (1958), pp. 280–287.

Grzegorczyk, A., Some Classes of Recursive Functions, Rozprawy Matematyczne No.4, Warsaw (1953).

Kino, A., On Provably Recursive Functions and Ordinal Recursive Functions, J. Math. Soc. Japan, Vol. 20, No. 3, (1968), pp. 456–476.

Kreisel, G., On the Interpretation of Non-Finitist Proofs, J. Symbolic Logic17 (1952), pp. 43–58.

Kreisel, G., Inessential Extensions of Heyting's Arithmetic by means of Functionals of Finite Types, abstract, J. Symbolic Logic,24 (1959), p. 284.

Löb, M. H., and Wainer, S. S., Hierarchies of Number-Theoretic Functions, this vol.

Péter, R., Recursive Functions, Academic Press (1967).

Robbin, J. W., Ph. D. Dissertation, Princeton University (1965).

Tait, W. W., Nested Recursion, Math. Annalen,143 (1961), pp. 236–250.

Tait, W. W., A Characterization of Ordinal Recursive Functions, abstract, J. Symbolic Logic,24 (1959), p. 325.