Transfer Principle

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.

Read more about Transfer Principle:  History, Transfer Principle For The Hyperreals, Example, Generalizations of The Concept of Number, Differences Between R and *R, Constructions of The Hyperreals, Statement, Three Examples

Other articles related to "transfer principle, principle":

Hyperreal Number - Use in Analysis - Calculus With Algebraic Functions
... As an example of the transfer principle, the statement that for any nonzero number x, 2x ≠ x, is true for the real numbers, and it is in the form required by the transfer principle, so it is also true for ... Similarly, the casual use of 1/0 = ∞ is invalid, since the transfer principle applies to the statement that division by zero is undefined ... In the hyperreal system, dx2 ≠ 0, since dx is nonzero, and the transfer principle can be applied to the statement that the square of any nonzero number is nonzero ...
Transfer Principle - Three Examples
... The well-ordering principle implies every nonempty internal subset of *N has a smallest member ...
Income Inequality Metrics - Properties of Inequality Metrics - Transfer Principle
... The Pigou–Dalton, or transfer principle, is the assumption that makes an inequality metric actually a measure of inequality ...
Elementary Calculus: An Infinitesimal Approach - Transfer Principle
... In the second edition Keisler introduces the extension principle and the transfer principle in the following form Every real statement that holds for ... Keisler then gives a few examples of real statements to which the principle applies Closure law for addition for any x and y, the sum x + y is defined ...

Famous quotes containing the words principle and/or transfer:

    I sincerely believe ... that banking establishments are more dangerous than standing armies, and that the principle of spending money to be paid by posterity, under the name of funding, is but swindling futurity on a large scale.
    Thomas Jefferson (1743–1826)

    No sociologist ... should think himself too good, even in his old age, to make tens of thousands of quite trivial computations in his head and perhaps for months at a time. One cannot with impunity try to transfer this task entirely to mechanical assistants if one wishes to figure something, even though the final result is often small indeed.
    Max Weber (1864–1920)