Geodesic
Some simple syntactical definition of all classes of Grzegorczyk hierarchy
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VI, Tome 40 (1974), pp. 127-130 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\widetilde E^n$ be the least class of primitive recursive functions which contains initial functions of $E^n$ [1] and is closed under substitution and special recursion (see def. 5). Then $\widetilde E^n=E^n$. 
@article{ZNSL_1974_40_a14,
     author = {S. V. Pakhomov},
     title = {Some simple syntactical definition of all classes of {Grzegorczyk} hierarchy},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {127--130},
     year = {1974},
     volume = {40},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a14/}
}
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S. V. Pakhomov. Some simple syntactical definition of all classes of Grzegorczyk hierarchy. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VI, Tome 40 (1974), pp. 127-130. http://geodesic.mathdoc.fr/item/ZNSL_1974_40_a14/