Appendix on Interpolation via translations: proofs as expected
نویسندگان
چکیده
Theorem 3.2 A consequence system (L,`) enjoys Craig interpolation with respect to an L-function var, if (i) there is a Craig generalized translation schema from (L,`) to another consequence system (L′,`′) with respect to var and an L′-function var′; (ii) (L′,`′) enjoys Craig interpolation with respect to var′. Proof: Let (h1, h2, h) be a Craig generalized translation schema from (L,`) to (L′,`′) via a consequence system (L◦,`◦), with respect to an L-function var and an L′-function var′. Assume that (L′,`′) enjoys Craig interpolation over var′. Suppose that Γ ` φ and var(Γ) ∩ var(φ) 6= ∅. Then h1(Γ) `′ h2(φ) and var′(h1(Γ)) ∩ var′(h2(φ)) 6= ∅
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