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
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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.
@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},
publisher = {mathdoc},
volume = {88},
year = {1979},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_88_a13/}
}
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/