  In this work, it is proved that a set of numbers closed under addition and
whose representations in a rational base numeration system is a rational
language is not a finitely generated additive monoid.
  A key to the proof is the definition of a strong combinatorial property on
languages : the bounded left iteration property. It is both an unnatural
property in usual formal language theory (as it contradicts any kind of pumping
lemma) and an ideal fit to the languages defined through rational base number
systems.
