Abstract

For the ring of integers of a totally real field of algebraic numbers, J. Robinson defined a set which is always {+∞} or of the form [λ, +∞) or (λ, +∞) for some real number λ ≥ 4. All known examples give either {+∞} or [4, +∞). In this paper, we construct infinitely many fields such that the set is an interval, but not equal to [4, +∞).