On Diophantine Equations Solvable in Models of Open Induction
Otero, Margarita
J. Symbolic Logic, Tome 55 (1990) no. 1, p. 779-786 / Harvested from Project Euclid
We consider IOpen, the subsystem of PA (Peano Arithmetic) with the induction scheme restricted to quantifier-free formulas. We prove that each model of IOpen can be embedded in a model where the equation $x^2_1 + x^2_2 + x^2_3 + x^2_4 = a$ has a solution. The main lemma states that there is no polynomial $f(x,y)$ with coefficients in a (nonstandard) DOR $M$ such that $|f(x,y)| < 1$ for every $(x,y) \in C$, where $C$ is the curve defined on the real closure of $M$ by $C: x^2 + y^2 = a$ and $a > 0$ is a nonstandard element of $M$.
Publié le : 1990-06-14
Classification: 
@article{1183743331,
     author = {Otero, Margarita},
     title = {On Diophantine Equations Solvable in Models of Open Induction},
     journal = {J. Symbolic Logic},
     volume = {55},
     number = {1},
     year = {1990},
     pages = { 779-786},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743331}
}
Otero, Margarita. On Diophantine Equations Solvable in Models of Open Induction. J. Symbolic Logic, Tome 55 (1990) no. 1, pp.  779-786. http://gdmltest.u-ga.fr/item/1183743331/