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Abstract. Ordinary first-order logic has the property that two formulas φ and ψ have the same meaning in a structure if and only if the formula φ ↔ ψ is true in the structure. We prove that independence-friendly logic does not have this property. §1. Introduction. The meaning of a first-order formula φ in a structure A is just the set of valuations that make the formula true in A. That is, φ A = {a ∈ N A | A | = φ[a]}, where A is the universe of A, and N is the number of variables in φ. Given a structure A and any two first-order formulas φ and ψ

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