Interpolation for a sequent calculus of generalized quantifiers

Abstract

Van Lambalgen (1991) proposed a translation from a language containing a generalized quantifier Q into a first-order language enriched with a family of predicates R _i, for every arity i (or an infinitary predicate R) which takes Qxφ(x,y ₁,...,y _n) to ∀x(R(x, y ₁,...,y _n) → φ(x,y ₁,..., y _n)) (y ₁,..., y _n are precisely the free variables of Qxφ). The logic of Q (without ordinary quantifiers) corresponds therefore to the fragment of first-order logic which contains only specially restricted quantification. We prove that this logic (and the corresponding fragment) has the interpolation property.