The rule of induction in the three variable arithmetic based on + and -
Annales de la faculté des sciences de l'université de Clermont. Mathématiques, Tome 35 (1967) no. 4, pp. 25-31. 
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     title = {The rule of induction in the three variable arithmetic based on $+$ and $-$},
     journal = {Annales de la facult\'e des sciences de l'universit\'e de Clermont. Math\'ematiques},
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     year = {1967},
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     url = {http://archive.numdam.org/item/ASCFM_1967__35_4_25_0/}
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Shepherdson, J. C. The rule of induction in the three variable arithmetic based on $+$ and $-$. Annales de la faculté des sciences de l'université de Clermont. Mathématiques, Tome 35 (1967) no. 4, pp. 25-31. http://archive.numdam.org/item/ASCFM_1967__35_4_25_0/

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Shepherdson J.C. [1] - A non standard model for a free variable fragment of number theory Bull. Acad. Polon. Sci. Ser Math. Astronom. Phys. 12 (1964) pp. 79-86. | MR | Zbl

Shepherdson J.C. [2] - Non Standard models for fragments of number theory, Proc. Int. sympodium on Model Theory, Berkeley 1963. | Zbl

Shoenfield J.R. [1] - Open sentences and the induction axiom, JSL, 23 (1958) pp. 7 -12. | MR | Zbl