In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure V by passing to a nonstandard enlargement ^* V of V is also provable without doing so, and vice versa." It is a result of Łoś' theorem and the completeness theorem for first-order predicate logic The transfer principle is stated as follows. Let V be a superstructure, let ^* V be an enlargement of V, let σ be any sentence in the language for (V, element ), and let ^* σ denote the ^*-transform of σ. Then (V, element )⊨σ if and only if (^* V, ^* element )⊨^* σ.
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