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Transfer Principle

المؤلف:  المرجع الالكتروني للمعلوماتيه

المصدر:  www.almerja.com

الجزء والصفحة:  ...

13-2-2022

1923

Transfer Principle

In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about a given superstructure  by passing to a nonstandard enlargement  of  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  be a superstructure, let  be an enlargement of , let  be any sentence in the language for , and let  denote the -transform of . Then  if and only if .