Diophantine Sets of Polynomials over Number Fields

28 January 2010
Jeroen Demeyer
<p class="MsoPlainText">&nbsp;</p><p class="MsoPlainText">Let R be a number field (or a recursive subring of anumber field) and consider the polynomial ring R[T].</p><p class="MsoPlainText">We show that the set of polynomials with integercoefficients is diophantine (existentially definable) over R[T].</p><p class="MsoPlainText">Applying a result by Denef, this implies that everyrecursively enumerable subset of R[T]^k is diophantine over R[T].</p>