Geodesic
Some properties of graphs of functions in the Grzegorczyk hierarchy
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 105-107 
S. V. Pakhomov. Some properties of graphs of functions in the Grzegorczyk hierarchy. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 105-107. http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a14/
@article{ZNSL_1972_32_a14,
     author = {S. V. Pakhomov},
     title = {Some properties of graphs of functions in the {Grzegorczyk} hierarchy},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--107},
     year = {1972},
     volume = {32},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a14/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\Gamma^n$ be the set of all primitive recursive functions whose graphs belong to $\varepsilon^n$ [I]. It is proved that $\Gamma^n$ is the closure of $\varepsilon^n$ relative to identification and permutation of variables, to substitution of constants and to special operations I)–4) on p.p. 105–106. In particular $f_n\in\Gamma^0$ for every $n\geq 3$. Here $f_n$ is a modification of Ackermana's function described in [I] p. 30.