Abstract

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