  For rings $\mathcal{O}_K$ of totally real algebraic integers, J. Robinson
defined a set which is always $\{+\infty\}$ or of the form $[\lambda,+\infty)$
or $(\lambda,+\infty)$ for some real number $\lambda\ge4$. All known examples
give either $\{+\infty\}$ or $[4,+\infty)$. In this paper, we construct
infinitely many fields such that the set is an interval, but not equal to
$[4,+\infty)$.
