Transfer Principle

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 sigma be any sentence in the language for (V, in ), and let ^*sigma denote the ^*-transform of sigma. Then (V, in )|=sigma if and only if (^*V,^* in )|=^*sigma.

See also

Łoś' theorem, Nonstandard Analysis

This entry contributed by Matt Insall (author's link)

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Insall, Matt. "Transfer Principle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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