The rule of induction in the three variable arithmetic based on + and -
Annales scientifiques de l'Université de Clermont. Mathématiques, Volume 35 (1967) no. 4, p. 25-31 
@article{ASCFM_1967__35_4_25_0,
     author = {Shepherdson, J. C.},
     title = {The rule of induction in the three variable arithmetic based on $+$ and $-$},
     journal = {Annales scientifiques de l'Universit\'e de Clermont. Math\'ematiques},
     publisher = {UER de Sciences exactes et naturelles de l'Universit\'e de Clermont},
     volume = {35},
     number = {4},
     year = {1967},
     pages = {25-31},
     mrnumber = {276089},
     language = {en},
     url = {http://www.numdam.org/item/ASCFM_1967__35_4_25_0}
}

Shepherdson, J. C. The rule of induction in the three variable arithmetic based on $+$ and $-$. Annales scientifiques de l'Université de Clermont. Mathématiques, Volume 35 (1967) no. 4, pp. 25-31. http://www.numdam.org/item/ASCFM_1967__35_4_25_0/

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