We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q1 is definable in terms of another quantifier Q2, 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 nondefinability results for second-order generalized quantifiers. In particular, we show that the monadic second-order majority quantifier Most 1 is not definable in second-order logic
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