Decidable Expansions of Labelled Linear Orderings
  Consider a linear ordering equipped with a finite sequence of monadic predicates. If the ordering contains an interval of order type \omega or -\omega, and the monadic second-order theory of the combined structure is decidable, there exists a non-trivial expansion by a further monadic predicate that is still decidable. 
Alexis Bes (University of Paris-Est Cr\'eteil), Alexander Rabinovich   (Tel-Aviv University, The Blavatnik School of Compute...
cs.LO math.LO