Classifications of recursive functions by means of hierarchies
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- Trans. Amer. Math. Soc. 104 (1962), 101-122 Request permission
References
- Paul Axt, On a subrecursive hierarchy and primitive recursive degrees, Trans. Amer. Math. Soc. 92 (1959), 85–105. MR 126377, DOI 10.1090/S0002-9947-1959-0126377-3
- Solomon Feferman, Transfinite recursive progressions of axiomatic theories, J. Symbolic Logic 27 (1962), 259–316. MR 172792, DOI 10.2307/2964649
- S. Feferman and C. Spector, Incompleteness along paths in progressions of theories, J. Symbolic Logic 27 (1962), 383–390. MR 172793, DOI 10.2307/2964544 D. Hilbert and P. Bernays, Grundlagen der Mathematik, Vol. II, Springer, Berlin, 1938.
- S. C. Kleene, Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc. 79 (1955), 312–340. MR 70594, DOI 10.1090/S0002-9947-1955-0070594-4
- S. C. Kleene, Extension of an effectively generated class of functions by enumeration, Colloq. Math. 6 (1958), 67–78. MR 118672, DOI 10.4064/cm-6-1-67-78
- S. C. Kleene, Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc. 61 (1955), 193–213. MR 70593, DOI 10.1090/S0002-9904-1955-09896-3
- S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals. II, Amer. J. Math. 77 (1955), 405–428. MR 70595, DOI 10.2307/2372632
- G. Kreisel, Non-uniqueness results for transfinite progressions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 287–290 (English, with Russian summary). MR 133230
- G. Kreisel, Ordinal logics and the characterization of informal concepts of proof. , Proc. Internat. Congress Math. 1958., Cambridge Univ. Press, New York, 1960, pp. 289–299. MR 0124194 J. Myhill, A stumblingblock in constructive mathematics, Abstract, J. Symb. Logic 18 (1953), 190-191. R. Péter, Rekursive Funktionen, rev. ed., Akademischer Verlag, Budapest, 1957.
- N. A. Routledge, Ordinal recursion, Proc. Cambridge Philos. Soc. 49 (1953), 175–182. MR 53046, DOI 10.1017/s0305004100028255
- Clifford Spector, Recursive well-orderings, J. Symbolic Logic 20 (1955), 151–163. MR 74347, DOI 10.2307/2266902
- W. W. Tait, Nested recursion, Math. Ann. 143 (1961), 236–250. MR 124214, DOI 10.1007/BF01342980
Additional Information
- © Copyright 1962 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 104 (1962), 101-122
- MSC: Primary 02.77
- DOI: https://doi.org/10.1090/S0002-9947-1962-0142453-3
- MathSciNet review: 0142453