The Hierarchy Theorem for Second Order Generalized Quantifiers

Journal of Symbolic Logic 71 (1):188 - 202 (2006)
Abstract
We study definability of second order generalized quantifiers on finite structures. Our main result says that for every second order type t there exists a second order generalized quantifier of type t which is not definable in the extension of second order logic by all second order generalized quantifiers of types lower than t
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