Geodesic
Positive rudimentarity of the graphs of the Ackermann's and Grzegorczyk's functions
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VIII, Tome 88 (1979), pp. 186-191 
A. V. Proskurin. Positive rudimentarity of the graphs of the Ackermann's and Grzegorczyk's functions. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VIII, Tome 88 (1979), pp. 186-191. http://geodesic.mathdoc.fr/item/ZNSL_1979_88_a13/
@article{ZNSL_1979_88_a13,
     author = {A. V. Proskurin},
     title = {Positive rudimentarity of the graphs of the {Ackermann's} and {Grzegorczyk's} functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {186--191},
     year = {1979},
     volume = {88},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_88_a13/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The graphs of the Ackermann's functions $\lambda xyg_n(x,y)$ [3,4] and the Grzegorczyk's functions $f_n$ [2] are shown to be in the class of the positive rudimentary predicates of J. H. Bennett [1]. The latter class is included in the initial class $\mathscr E_*^0$ A. Grzegorczyk [2], thus our result strengthens that of S. V. Pakhomov [5] about the expressibility of the $f_n$'s graphs in $\mathscr E_*^0$. By a generalization of the method applied, the positive rudimentarity of the graph of the Ackerman's function $\lambda nxyg_n(x,y)$ can be proved.