References
L. Maliaukienė, The provability of the double induction axiom in the additive arithmetic,Lith. Math. J.,35, 518–526 (1995).
J. R. Shoenfield, Open sentences and the induction axiom,JSL,23, 7–12 (1958).
J. C. Shepherdson. A non-standard model for a free variable fragments of number theory,Bull. Acad. Pol. Sci.,12, 79–86 (1964).
J. C. Shepherdson, The rule of induction in the free variable arithmetic based on + and.Ann. Fac. Sci. Univ. Clermont-Fernand II Math.,4, 25–31 (1967).
Additional information
Vilnius Pedagogical University, Studentų 39. 2034 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 37, No. 1, pp. 61–70, January–March, 1997.
Rights and permissions
About this article
Cite this article
Maliaukienė, L. The constructive provability of a restricted axiom of double induction in the free variable additive arithmetic. Lith Math J 37, 46–53 (1997). https://doi.org/10.1007/BF02465439
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02465439