Abstract
The representability is proved of the graphs of the W. Ackermann functions λxy. gn(x, y) and the A. Grzegorczyk functions fn in the class of positive rudimentary predicates of J. H. Bennett, found in the initial class
of A. Grzegorczyk. This essentially improves a result of S. V. Pakhomov on the representability of the graphs of fn in
. A generalization of the method of proof allows one to prove the positive rudimentarity of the graph of the W. Ackermann function λnxy · gn(x, y).
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 186–191, 1979.
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Proskurin, A.V. Positive rudimentarity of the graphs of Ackermann and Grzegorczyk. J Math Sci 20, 2363–2366 (1982). https://doi.org/10.1007/BF01629447
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DOI: https://doi.org/10.1007/BF01629447