Interpolation for a sequent calculus of generalized quantifiers
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 Ri, for every arity i (or an infinitary predicate R) which takes Qxφ(x,y1,...,yn) to ∀x(R(x, y1,...,yn) → φ(x,y1,..., yn)) (y1,..., yn 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.
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