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Concept in model theory
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
Transfer_principle
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
hyperreal numbers satisfy the transfer principle, a rigorous version of Leibniz's heuristic law of continuity. The transfer principle states that true first-order
Hyperreal_number
Geometric theorem
In geometry, Hesse's principle of transfer (German: Übertragungsprinzip) states that if the points of the projective line P1 are depicted by a rational
Hesse's_principle_of_transfer
Calculus using a logically rigorous notion of infinitesimal numbers
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
Nonstandard_analysis
1976 mathematics textbook by H. Jerome Keisler
In the second edition Keisler introduces the extension principle and the transfer principle in the following form: Every real statement that holds for
Elementary Calculus: An Infinitesimal Approach
Elementary_Calculus:_An_Infinitesimal_Approach
Principle that whatever succeeds for the finite also succeeds for the infinite
infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in
Law_of_continuity
Extremely small quantity in calculus; thing so small that there is no way to measure it
hyperreals implement an infinitesimal-enriched continuum and the transfer principle implements Leibniz's law of continuity. The standard part function
Infinitesimal
Modern application of infinitesimals
π. Now let the index n be an infinite hypernatural number. By the transfer principle, the natural extension of the Dirichlet function takes the value 1
Nonstandard_calculus
Topics referred to by the same term
language Transfer of learning, in education Transfer function in mathematics Transfer (group theory), a type of homomorphism Transfer principle, in mathematics
Transfer
Theorem in mathematical logic
k.} This completes the proof. The Lefschetz principle, one of the first examples of a transfer principle, extends this result. A first-order sentence
Compactness_theorem
German mathematician (1811–1874)
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
Otto_Hesse
Hyperreal number that is equal to its own integer part
all real x and equals the greatest integer not exceeding x. By the transfer principle of nonstandard analysis, there exists a natural extension: ∗ ⌊ ⋅ ⌋
Hyperinteger
Modern reformulation of the calculus in terms of infinitesimals
nonstandard analysis in its use of nonclassical logic, and in lacking the transfer principle. Some theorems of standard and nonstandard analysis fail in smooth
Smooth_infinitesimal_analysis
Geometrical concept relating area and volume
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: 2-dimensional
Cavalieri's_principle
Passive heat exchanger that transfers heat
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
Heat_sink
Axiom of set theory
The principle is thus not available in constructive set theory, where non-classical logic is employed. The situation is different when the principle is
Axiom_of_choice
Type of set in mathematical logic
model. The concept of internal sets is a tool in formulating the transfer principle, which concerns the logical relation between the properties of the
Internal_set
Paradox in set theory
an unrestricted comprehension principle leads to contradictions. According to the unrestricted comprehension principle, for any sufficiently well-defined
Russell's_paradox
ultraproduct construction to construct the hyperreals and prove the transfer principle. 1955 - Pyotr Novikov finds a (finitely presented) group whose word
Timeline of mathematical logic
Timeline_of_mathematical_logic
Swiss mathematician (1707–1783)
modern standards of mathematical rigour (in particular his reliance on the principle of the generality of algebra), his ideas led to many great advances. Euler
Leonhard_Euler
Logic theorem
noncontradiction (LNC; also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that for any given proposition
Law_of_noncontradiction
Biological process
within the same flower, distinguished from geitonogamous pollination, transfer of pollen to a different flower on the same flowering plant, or within
Reproduction
French mathematician (1789–1857)
the "Principle of the argument" in many modern textbooks on complex analysis. In modern control theory textbooks, the Cauchy argument principle is quite
Augustin-Louis_Cauchy
Mathematical notion of infinitesimal difference
and quite intuitive approach to calculus using infinitesimals, see transfer principle. The notion of a differential motivates several concepts in differential
Differential_(mathematics)
French mathematician and lawyer (1601–1665)
geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory,
Pierre_de_Fermat
Parties to a transaction are on an equal footing
double tax conventions, through transfer pricing, among each other. Transfer pricing and the arm's length principle were one of the focal points of the
Arm's_length_principle
Principle relating to fluid dynamics
Bernoulli's principle is a concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally, Bernoulli's
Bernoulli's_principle
Mathematical formulation of vector pairs used in physics (rigid body dynamics)
addition of vectors. Important theorems of screw theory include: the transfer principle proves that geometric calculations for points using vectors have parallel
Screw_theory
Electrical transmission without physical connection
Transfer principle which presented by MIT". ニコラテスラって素晴らしい. 30 March 2017. Sara Linder (2 May 2021), Interference Risks from Wireless Power Transfer for
Wireless_power_transfer
Logical principle
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
Law_of_excluded_middle
Process of repeating items in a self-similar way
logic Strength Theories of truth semantic Tarski's Kripke's T-schema Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability
Recursion
Foundational principle in quantum physics
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is
Uncertainty_principle
Two closely related mathematical subjects
matpur.2023.05.004. S2CID 119702436. Kuhlmann, F.-V. (2001) [1994], "Transfer principle", Encyclopedia of Mathematics, EMS Press Neeman, Amnon (2007). Algebraic
Algebraic geometry and analytic geometry
Algebraic_geometry_and_analytic_geometry
Ways inequality is measured
x\sqcup 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
Income_inequality_metrics
Non-contradiction of a theory
logic Strength Theories of truth semantic Tarski's Kripke's T-schema Transfer principle Truth predicate Truth value Type Ultraproduct Validity Computability
Consistency
Real numbers adjoined with a nil-squaring element
introducing dual numbers into physics follows from the Pauli exclusion principle for fermions. The direction along ε is termed the "fermionic" direction
Dual_number
Physical lower limit to energy consumption of computation
Landauer's principle is a physical principle pertaining to a lower theoretical limit of energy consumption of computation. It holds that an irreversible
Landauer's_principle
Theory of truth in the philosophy of language
predicates) with the strong Kleene evaluation scheme. Disquotational principle Semantics of logic T-schema Triune continuum paradigm Hale, Bob; Wright
Semantic_theory_of_truth
Form of mathematical proof
with the induction principle uniquely model the natural numbers. Replacing the induction principle with the well-ordering principle allows for more exotic
Mathematical_induction
Rules and methods for pricing transactions between enterprises under common ownership
intragroup transfer prices that differ from what would have been charged by unrelated enterprises dealing at arm’s length (the arm’s-length principle). The
Transfer_pricing
German polymath (1646–1716)
belated vindication of Leibniz's mathematical reasoning. Robinson's transfer principle is a mathematical implementation of Leibniz's heuristic law of continuity
Gottfried_Wilhelm_Leibniz
Philosophical problem-solving principle
problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements. It is also known as the principle of parsimony
Occam's_razor
18th-century argument in mathematics
known to be true by Fourier analysis.[example needed] Principle of permanence Transfer principle Jahnke, Hans Niels (2003), A history of analysis, American
Generality_of_algebra
football transfers, which details the highest transfer fees ever paid for players and managers, as well as transfers which set new world transfer records
List of most expensive association football transfers
List_of_most_expensive_association_football_transfers
Mathematical construction
theorem – Existence and cardinality of models of logical theories Transfer principle – Concept in model theory Ultrafilter – Maximal proper filter Leinster
Ultraproduct
American mathematician
Robinson's joint consistency theorem – Theorem of mathematical logic Transfer principle – Concept in model theory O'Connor, John J.; Robertson, Edmund F.
Abraham_Robinson
Phenomenon within psychotherapy
inappropriate without proper clinical supervision. It is common for people to transfer feelings about their parents to their partners or children (that is, cross-generational
Transference
Method of deriving conclusions
interpreted broadly to include general standards of research, such as the principle that scientific experiments should be replicable. One of the first discussions
Rule_of_inference
Branch of mathematics
solutions are known as geodesics. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points
Calculus
Algebraic manipulation of "true" and "false"
All these definitions of Boolean algebra can be shown to be equivalent. Principle: If (X, R) is a partially ordered set, then (X, R(inverse)) is also a
Boolean_algebra
Statement that is taken to be true
inference) was developed by the ancient Greeks, and has become the core principle of modern mathematics. Tautologies excluded, nothing can be deduced if
Axiom
In logic, a statement which is always true
not-B, then not-A must be false, then A must be true"), which is the principle known as reductio ad absurdum. For instance, "If it's not bound, we know
Tautology_(logic)
Design principle for computer networking
The end-to-end (E2E) principle is a design principle in computer networking that requires application-specific features (such as reliability and security)
End-to-end_principle
Experiment demonstrating transfer of genetic information
"transforming principle" that was somehow part of the dead III-S strain bacteria. Scientific advances since then have revealed that the "transforming principle" Griffith
Griffith's_experiment
Passenger transport helicopter
Helicopters and Korean Aerospace Industries (KAI) formed an agreement to transfer principle manufacturing activity for the EC155 to South Korea; KAI shall become
Eurocopter_EC155
Measure of inequality of a statistical distribution
people in the income distribution, which allows the Gini to meet the Transfer Principle. Note that the Jasso-Deaton formula rescales the coefficient so that
Gini_coefficient
Principle that Internet service providers should treat all data equally
Net neutrality, sometimes referred to as network neutrality, is the principle that Internet service providers (ISPs) must treat all Internet communications
Net_neutrality
existence of the "transfer idea". According to Morris, while not discounting other reasons for the exodus, the "transfer principle" theory suggests that
Causes of the 1948 Palestinian expulsion and flight
Causes_of_the_1948_Palestinian_expulsion_and_flight
Measure of algorithmic complexity
incompressible by 1 is said to be simply incompressible – by the pigeonhole principle, which applies because every compressed string maps to only one uncompressed
Kolmogorov_complexity
Class of formal logics
middle and double negation elimination Law of noncontradiction, and the principle of explosion Monotonicity of entailment and idempotency of entailment
Classical_logic
Limitative results in mathematical logic
recursively enumerable. This means that there is a computer program that, in principle, could enumerate all the theorems of the system without listing any statements
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Principle in kinetic systems
thermodynamics, the principle of detailed balance says that every process of energy transfer in one direction must also allow energy transfer in the opposite
Detailed_balance
In mathematics, a statement that has been proven
or principle is a theorem with wide applicability (e.g. the law of large numbers, law of cosines, Kolmogorov's zero–one law, Harnack's principle, the
Theorem
Testing device for logical soundness
that Bill believes"—on the righthand side of the logical biconditional. Principle of bivalence Law of excluded middle Künne, Wolfgang (2003). Conceptions
T-schema
Standard system of axiomatic set theory
constructibility (V=L) (which is also not a ZFC axiom) Continuum hypothesis Diamond principle Martin's axiom (which is not a ZFC axiom) Suslin hypothesis Remarks: The
Zermelo–Fraenkel_set_theory
2003 book by James Paul Gee
Discovery Principle: The learner is told very little explicitly, and is instead allowed to explore and discover on his/her own. Transfer Principle: Learners
What Video Games Have to Teach Us About Learning and Literacy
What_Video_Games_Have_to_Teach_Us_About_Learning_and_Literacy
Yes-or-no question that cannot ever be solved by a computer
theory. In 1977, Paris and Harrington proved that the Paris-Harrington principle, a version of the Ramsey theorem, is undecidable in the axiomatization
Undecidable_problem
Heuristic principle enunciated by Gottfried Wilhelm Leibniz
mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled
Transcendental law of homogeneity
Transcendental_law_of_homogeneity
Subfield of automated reasoning and mathematical logic
mathematical truth using axioms and inference rules of formal logic, in principle opening up the process to automation. In 1920, Thoralf Skolem simplified
Automated_theorem_proving
Function that preserves distinctness
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
Injective_function
Branch of mathematics that studies sets
number of...', or N x : F x {\displaystyle Nx:Fx} ), relying on Hume's principle. However, Frege's work was short-lived, as it was found by Bertrand Russell
Set_theory
Proof technique in nonstandard analysis
hypernatural numbers. Overspill principle—Consider a first-order theory T {\displaystyle T} of Peano arithmetic and an induction principle, optionally restricted
Overspill
Set of elements in any of some sets
Disjoint union – In mathematics, operation on sets Inclusion–exclusion principle – Counting technique in combinatorics Intersection (set theory) – Set
Union_(set_theory)
Obsolete theories in natural history and natural philosophy
than empirical reasons and promoted by force. Spontaneous generation – a principle regarding the spontaneous generation of complex life from inanimate matter
List of superseded scientific theories
List_of_superseded_scientific_theories
Mathematical logic concept
system, today called "primitive recursive arithmetic with the additional principle of quantifier-free transfinite induction up to the ordinal ε0", is neither
Gentzen's_consistency_proof
Reasoning for mathematical statements
previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known
Mathematical_proof
Core concept in libertarianism
The non-aggression principle (NAP) is a concept in which "aggression"—defined as initiating or threatening any forceful interference with an individual
Non-aggression_principle
Properties linking logical conjunction and disjunction
duality between conjunction and disjunction, also called the duality principle. It is the most widely known example of duality in logic. The duality
Conjunction/disjunction duality
Conjunction/disjunction_duality
Function from the limited hyperreal to the real numbers
numbers Surreal numbers Individual concepts Standard part function Transfer principle Hyperinteger Increment theorem Monad Internal set Levi-Civita field
Standard_part_function
Index to measure economic inequality
income's ratio more than it changes the larger income's ratio, the transfer-principle is satisfied by this index. Equivalently, if the situation is characterized
Theil_index
Computation model defining an abstract machine
feature, which allows them to be Turing complete in principle. It is just Turing complete in principle, as memory allocation in a programming language is
Turing_machine
Mathematical set containing no elements
EMPTY SET may be used instead. In standard axiomatic set theory, by the principle of extensionality, two sets are equal if they have the same elements (that
Empty_set
Category of mathematical proof
that therefore there must be a smallest solution (by the Well-ordering principle). From the alleged smallest solution, it is then shown that a smaller
Proof_of_impossibility
Multi-winner electoral system
The single transferable vote (STV) or proportional-ranked choice voting (P-RCV), also known as PR-STV and "proportional representation by means of the
Single_transferable_vote
Principle of atomic physics
quantum chemistry, the Aufbau principle (pronounced /ˈaʊfbaʊ/, from German: Aufbauprinzip, lit. 'building-up principle'), also called the Aufbau rule
Aufbau_principle
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
that the variance and mean both obey this principle. Pigou–Dalton transfer principle: when wealth is transferred from a wealthier agent i to a poorer agent
Coefficient_of_variation
Subfield of mathematics
called Zermelo–Fraenkel set theory (ZF). Zermelo's axioms incorporated the principle of limitation of size to avoid Russell's paradox. In 1910, the first volume
Mathematical_logic
Axioms for the natural numbers
operation. The ninth, final, axiom is a second-order statement of the principle of mathematical induction over the natural numbers, which makes this formulation
Peano_axioms
x ) {\displaystyle \varphi (x)} with one free variable, the induction principle for φ {\displaystyle \varphi } expresses the validity of mathematical
Induction, bounding and least number principles
Induction,_bounding_and_least_number_principles
Type of mathematical proof
theorem is only true by coincidence, and not because of some underlying principle or connection. Other types of proofs—such as proof by induction (mathematical
Proof_by_exhaustion
Logical connective OR
problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well as the numerous mismatches between classical disjunction and
Logical_disjunction
3-volume treatise on mathematics, 1910–1913
⊦: p ∨ p .⊃. p. Pp principle of tautology ✱1.3. ⊦: q .⊃. p ∨ q. Pp principle of addition ✱1.4. ⊦: p ∨ q .⊃. q ∨ p. Pp principle of permutation ✱1.5.
Principia_Mathematica
Size of a possibly infinite set
this requirement is sometimes called the axiom of cardinality or Hume's principle. It will be shown later that such a function can be constructed without
Cardinal_number
Mathematical construction of a set with an equivalence relation
A given proposition may have many proofs, of course; according to the principle of proof irrelevance, normally only the truth of the proposition matters
Setoid
Kind of transfinite induction
set-induction, is a principle that can be used to prove that all sets satisfy a given property. Considered as an axiomatic principle, it is called the axiom
Epsilon-induction
Identities and relationships involving sets
extremely important and powerful property of set algebra, namely, the principle of duality for sets, which asserts that for any true statement about sets
Algebra_of_sets
Mathematical proposition equivalent to the axiom of choice
two. An earlier formulation of Zorn's lemma is the Hausdorff maximal principle which states that every totally ordered subset of a given partially ordered
Zorn's_lemma
a legal principle that governs the automatic transfer of a deceased person's property, rights, and obligations to their heirs. This principle is notably
Saisine
Mathematical term; concerning axioms used to derive theorems
mechanics and mathematical logic. It did so by taking on as its methodical principle the axiomatic method that was to revolutionise the science of [the twentieth
Axiomatic_system
Set of sentences in a formal language
In a deductive system (such as first-order logic) that satisfies the principle of explosion, this is equivalent to requiring that there is no sentence
Theory_(mathematical_logic)
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TRANSFER PRINCIPLE
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TRANSFER PRINCIPLE
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