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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, which states that any sentence in the first-order language of fields that is true for the complex numbers is also true for any algebraically closed field of characteristic 0.

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Transfer principle

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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...

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Hyperreal number

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hyperreal numbers satisfy the transfer principle, a rigorous version of Leibniz's heuristic law of continuity. The transfer principle states that true first-order...

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Transfer

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language Transfer of learning, in education Transfer function in mathematics Transfer (group theory), a type of homomorphism Transfer principle, in mathematics...

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Infinitesimal

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hyperreals implement an infinitesimal-enriched continuum and the transfer principle implements Leibniz's law of continuity. The standard part function...

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Nonstandard analysis

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argued that this law of continuity of Leibniz's is a precursor of the transfer principle. Robinson continued: However, neither he nor his disciples and successors...

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Otto Hesse

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group, Hessian pairs, Hesse's theorem, Hesse pencil, and the Hesse transfer principle are named after him. Many of Hesse's research findings were presented...

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Overspill

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numbers. By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction: For any internal...

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Nonstandard calculus

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natural hyperreal extension usually denoted f* (see discussion of Transfer principle in main article at nonstandard analysis). Using the notation ≈ {\displaystyle...

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Law of continuity

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infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in...

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Hyperinteger

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all real x and equals the greatest integer not exceeding x. By the transfer principle of nonstandard analysis, there exists a natural extension: ∗ ⌊ ⋅ ⌋...

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Law of excluded middle

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In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is...

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Heat sink

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sink (also commonly spelled heatsink,) is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid...

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Compactness theorem

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k.} This completes the proof. The Lefschetz principle, one of the first examples of a transfer principle, extends this result. A first-order sentence...

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Income inequality metrics

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x} is the union of x with (a copy of) itself. Transfer principle The Pigou–Dalton, or transfer principle, is the assumption that makes an inequality metric...

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Causes of the 1948 Palestinian expulsion and flight

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existence of the "transfer idea". According to Morris, while not discounting other reasons for the exodus, the "transfer principle" theory suggests that...

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Law of noncontradiction

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(LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions...

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Internal set

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model. The concept of internal sets is a tool in formulating the transfer principle, which concerns the logical relation between the properties of the...

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Axiom of choice

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The principle is thus not available in constructive set theory, where non-classical logic is employed. The situation is different when the principle is...

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Uncertainty principle

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The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is...

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Gottfried Wilhelm Leibniz

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belated vindication of Leibniz's mathematical reasoning. Robinson's transfer principle is a mathematical implementation of Leibniz's heuristic law of continuity...

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Wireless power transfer

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Wireless power transfer (WPT), wireless power transmission, wireless energy transmission (WET), or electromagnetic power transfer is the transmission of...

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Injective function

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graph is never intersected by any horizontal line more than once. This principle is referred to as the horizontal line test. Functions with left inverses...

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Algebraic geometry and analytic geometry

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matpur.2023.05.004. S2CID 119702436. Kuhlmann, F.-V. (2001) [1994], "Transfer principle", Encyclopedia of Mathematics, EMS Press Neeman, Amnon (2007). Algebraic...

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Screw theory

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addition of vectors. Important theorems of screw theory include: The Transfer Principle proves that geometric calculations for points using vectors have parallel...

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Recursion

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logic Strength Theories of truth semantic Tarski's Kripke's T-schema Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability...

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