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We study the expressive power of open formulas of dependence logic introduced in Väänänen [Dependence logic (Vol. 70 of London Mathematical Society Student Texts), 2007]. In particular, we answer a question raised by Wilfrid Hodges: how to characterize the sets of teams definable by means of identity only in dependence logic, or equivalently in independence(More)
The concept of a generalized quantiier of a given similarity type was deened in Lin66]. Our main result says that on nite structures diierent similarity types give rise to diierent classes of generalized quantiiers. More exactly, for every similarity type t there is a generalized quantiier of type t which is not deenable in the extension of rst order logic(More)