3 papers
math.NT2004
Elliptic divisibility sequences and undecidable problems about rational points
Gunther Cornelissen, Karim Zahidi
Julia Robinson has given a first-order definition of the rational integers Z in the rational numbers Q by a formula (\forall \exists \forall \exists)(F=0) where the \forall-quantif…
math.NT2003
Division-ample sets and the Diophantine problem for rings of integers
Gunther Cornelissen, Thanases Pheidas, Karim Zahidi
We prove that Hilbert's Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called division…
math.LO2000
Topology of Diophantine Sets: Remarks on Mazur's Conjectures
Gunther Cornelissen, Karim Zahidi
We show that Mazur's conjecture on the real topology of rational points on varieties implies that there is no diophantine model of the rational integers in the rational numbers. We…