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A new hierarchy of elementary functions


Author: G. T. Herman
Journal: Proc. Amer. Math. Soc. 20 (1969), 557-562
MSC: Primary 02.77
DOI: https://doi.org/10.1090/S0002-9939-1969-0250878-2
MathSciNet review: 0250878
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  • [1] P. Axt, Enumeration and the Grzegorczyk hierarchy, Z. Math. Logik Grundlagen Math. 9 (1963), 53-65. MR 0144811 (26:2352)
  • [2] J. P. Cleave, A hierarchy of primitive recursive functions, Z. Math. Logik Grundlagen Math. 9 (1963), 331-345. MR 0159754 (28:2970)
  • [3] P. C. Fischer, On formalisms for Turing machines, J. Assoc. Comput. Mach. 12 (1965), 570-580. MR 0191826 (33:53)
  • [4] A. Grzegorczyk, Some classes of recursive functions, Rozprowy Matematyczne 4 (1953), 1-44. MR 0060426 (15:667d)
  • [5] G. T. Herman, Turing machines and their applications to Hilbert's tenth problem, M.Sc. Thesis, University of London, 1964.
  • [6] -, A definition of simulation for discrete computing systems, Third Internat. Congr. for Logic, Methodology and Philosophy of Science, Amsterdam, 1967.
  • [7] -, On hierarchies of elementary functions, Proc. Internat. Colloq. Recursive Functions and their Applications (Tihany, 1967), Institut Blaise Pascal, Paris and Bolyai Janos Matematikai Tarsulat, Budapest, (in press).
  • [8] R. W. Ritchie, Classes of predictably computable functions, Trans. Amer. Math. Soc. 106 (1963), 139-173. MR 0158822 (28:2045)
  • [9] C. E. Shannon, A universal Turing machine with two internal states, Automata Studies, Ann. of Math Studies No. 34, Princeton Univ. Press, Princeton, N. J., 1956, pp. 157-165. MR 0079548 (18:103e)
  • [10] J. C. Shepherdson and H. E. Sturgis, Computability of recursive functions, J. Assoc. Comput. Mach. 10 (1963), 217-255. MR 0151374 (27:1359)

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DOI: https://doi.org/10.1090/S0002-9939-1969-0250878-2
Article copyright: © Copyright 1969 American Mathematical Society

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