 So generalized quantifiers remain a simple and versatile way of adding expressive power to FO. One natural question was if the logical characterization of PTIME mentioned above could be improved using generalized quantifiers, in particular if one could remove the restriction to ordered structures in this way. The answer, however, turned out to be negative, since Hella (1989) proved that the PTIME computable properties of arbitrary finite structures cannot be characterized by adding a finite number of generalized quantifiers to FO, or even to \(\FO(\LFP)\). The question of whether PTIME can be characterized by a logic of the form \(\FO^*(Q)\) remains open, however (indeed, solving it would be a major breakthrough in complexity theory).