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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