Sur les ensembles d'entiers reconnaissables
  Let U and V be two Bertrand numeration systems, and, a and b the two Parry numbers there are naturally associated with. Suppose they are multiplicatively independent. We prove that, if E is a subset of positive integers which is both U and V recognizable, then E is a finite union of arithmetical progressions. 
Fabien Durand (LAMFA)