Decidable Sentences Over Polynomial Rings
Shih-Ping Tung · Proceedings of the American Mathematical Society · 1988
Let $R$ be an algebraic number field or an algebraic integer ring. We prove that there is an algorithm to determine whether the sentence $\forall x\exists y\phi \left ( {x,y} \right )$, with $\phi \left ( {x,y} \right )$ a quantifier free formula over $R\left [ T \right ]$, is true in the polynomial ring $R\left [ T \right ]$ or not.