A characterization of definability of second-order generalized quantifiers with applications to non-definability

摘要

We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q_1 is definable in terms of another quantifier Q_2. the base logic being monadic second-order logic, reduces to the question if a quantifier Q_1~* is definable in FO(Q_2~*,＜,+, ×) for certain first-order quantifiers Q_1~* and Q_2~*. We use our characterization to show new definability and non-definability results for second-order generalized quantifiers. We also show that the monadic second-order majority quantifier Most is not definable in second-order logic.