Some rings have the same diophantine theory as $\mathbb{Z}$
Mihai Prunescu
University of Bucharest & Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Abstract:
Different methods of logic and model theory are applied to diophantine problems.
Several rings with the same diophantine theory as $\mathbb{Z}$ are produced,
and some of them have unusual properties: neither $\mathbb{Z}$, nor some usual
logical relations, are diophantine in those rings.