, Volume 6, Issue 3, pp 305-335

Definability of Polyadic Lifts of Generalized Quantifiers

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Abstract

We study generalized quantifiers on finite structures.With every function \(f\) : ω → ωwe associate a quantifier Q \(_{\text{f}} \) by letting Q \(_{\text{f}} \) xϕ say “there are at least \(_{\text{f}} \) (n) elementsx satisfying ϕ, where n is the sizeof the universe.” This is the general form ofwhat is known as a monotone quantifier of type < 1 >.We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of simpler quantifiers.