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/

Kreisel G. [1 ] - Application of mathematical logic to various branches of mathematics, Colloque de Logique Mathematique, Paris (1954), pp. 37-49. | MR 67825 | Zbl 0057.24502

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 161798 | Zbl 0132.24701

Shepherdson J.C. [2] - Non Standard models for fragments of number theory, Proc. Int. sympodium on Model Theory, Berkeley 1963. | Zbl 0154.26202

Shoenfield J.R. [1] - Open sentences and the induction axiom, JSL, 23 (1958) pp. 7 -12. | MR 99285 | Zbl 0085.24505