High Quality Content by WIKIPEDIA articles! In model theory, a transfer principle states that all statements of some language that are true for some structure, are true for another structure. One of the first examples was the Lefschetz principle, stating that any sentence in the first-order language of fields true for the complex numbers is also true for any algebraically closed field of characteristic 0. Its most common use is in Abraham Robinson's non-standard analysis of the hyperreal numbers, where the transfer principle states that any sentence expressible in a certain formal language that is true of real numbers is also true of hyperreal numbers. The transfer principle concerns the logical relation between the properties of the real numbers R, and the properties of a larger field denoted *R called the hyperreals. The field *R includes, in particular, infinitesimal ("infinitely small") numbers, providing a rigorous mathematical realisation of a project initiated by Leibniz.

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