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1-1 function change of variables completes the proof constant Corollary define existential quantifier F G pj first-order formula first-order language first-order logic first-order predicate calculus first-order representable first-order variable formula f function symbols functions f h and h1 Hence Henkin prefixes k-place predicate symbol k-selection Let f Let Q linear prefix normal forms normal representability number of quantifiers numbers of universal obtain occur in Q P-atom P(VO P(VQ Peano arithmetic predicate or function prefix Q pure predicate calculus Q and Q Q are Henkin Q fy Q is representable Q is weakly Q or Q Q P(n Q P(v quantifier-free formula quantifiers of Q r e n+1 representable by Q respective numbers selection function Skolem form Skolem functions standard prefix subprefix t e m+1 U R(F variables of Q vk_1 vocabulary weakly representable