Geodesic
A complete arithmetical system
Algebra i logika, Tome 6 (1967) no. 2, pp. 5-11 
N. V. Beliakin. A complete arithmetical system. Algebra i logika, Tome 6 (1967) no. 2, pp. 5-11. http://geodesic.mathdoc.fr/item/AL_1967_6_2_a0/
@article{AL_1967_6_2_a0,
     author = {N. V. Beliakin},
     title = {A complete arithmetical system},
     journal = {Algebra i logika},
     pages = {5--11},
     year = {1967},
     volume = {6},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_1967_6_2_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper is proved the completeness of an arithmetical system based on the notion of regularity, founded by P. S. Novikoff [1]. The proof of completeness used the classical logic but all the metamathematical notions are expressible in the dementary language of arithmetic.