The hierarchy theorem for generalized quantifiers

Journal of Symbolic Logic 61 (3):802-817 (1996)
Abstract
The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type t there is a generalized quantifier of type t which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than t. This was proved for unary similarity types by Per Lindström [17] with a counting argument. We extend his method to arbitrary similarity types
Keywords generalized quantifier   finite model theory   abstact model theory
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