Logic for Unambiguous Context-Free Languages

We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th'erien [18] based on implicit definability is used for this aim. We obtain a new connection between two undecidable problems, a logical one and a language theoretical one.