Languages extending l(q)

Abstract

We present a survey of the model theory of the quantifiers Qn and Qm,n, where [Formula Matemática]means that there is a K-powered subset X of M such that M [Formula Matemática] whenever a1 ,... an ∈ X, and [Formula Matemática] means that there is a K powered subset X of M such that[Formula Matemática] whenever a1 ,... an ∈ X and b1,..., bn ∉ X. Somerecent results are announced and several open problems are given.