Abstract

The quantifier Q m,n binds m + n variables. In the κ-interpretation $M \models Q^{m,n} \bar{x}, \bar{y}\phi\bar{x}, \bar{y}$ means that there is a κ-powered proper subset X of |M| such that whenever ā ∈ mX and b̄ ∈ n X̃ then $M \models \phi\bar{a}, \bar{b}$. If σ ∈ L m,n has a model in the κ-interpretation does it have a model in the λ-interpretation? For σ ∈ L 1,1, κ regular and uncountable, and λ = ω 1 the answer is yes.