Definability of Polyadic Lifts of Generalized Quantifiers

Abstract

We study generalized quantifiers on finite structures. With every function f : ω → ω we associate a quantifier Q_f by letting Q_fx p say ’’there are at least f(n) elementsx satisfying p, where n is the size of the universe.‘‘ This is the general form of what is known as a monotone quantifier of type 〈 1 〉. We study so called polyadic lifts of such quantifiers. The particular lifts we consider are Ramseyfication, branching and resumption. In each case we get exact criteria for definability of the lift in terms of simpler quantifiers.