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In mathematical logic, Craig's theorem (also known as Craig's trick) states that any recursively enumerable set of well-formed formulas of a first-order
Craig's_theorem
In mathematics, a statement that has been proven
undefinability theorem Church-Turing theorem of undecidability Löb's theorem Löwenheim–Skolem theorem Lindström's theorem Craig's theorem Cut-elimination theorem The
Theorem
Theorem in mathematical logic
mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if
Craig_interpolation
Property of logical theories
if and only if it is recursively axiomatizable, a result known as Craig's theorem.) A first-order formula with one universal quantification has the fmp
Finite_model_property
Conservativity theorem (mathematical logic) Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic) Cut-elimination theorem (proof
List_of_theorems
Theorem in physical cosmology
The Borde–Guth–Vilenkin (BGV) theorem is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout
Borde–Guth–Vilenkin_theorem
2013 film by Terry Gilliam
The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges.
The_Zero_Theorem
American philosopher (1918–2016)
97. Craig is particularly remembered in two theorems that bear his name: the Craig interpolation theorem, and Craig's theorem, also known as Craig's axiomatization
William_Craig_(philosopher)
Continuous function on an interval takes on every value between its values at the ends
In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval
Intermediate_value_theorem
Philosophical argument for the existence of God
quoted in Craig and Moreland, 2009: 143 William Lane Craig. ""Honesty, Transparency, Full Disclosure" and the Borde-Guth-Vilenkin Theorem". Reasonable
Kalam_cosmological_argument
Topics referred to by the same term
theorem may refer to: Craig interpolation in logic Marcinkiewicz interpolation theorem about non-linear operators Riesz–Thorin interpolation theorem about
Interpolation_theorem
Meta-scientific perspective
axiomatizability in restricted vocabularies, 'theoretical terms', Craig’s theorem, 'reduction sentences', 'empirical languages', Ramsey and Carnap sentences
Semantic_view_of_theories
Theorem in set theory
In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there
Schröder–Bernstein_theorem
American actress, mathematics writer, and education advocate (born 1975)
\mathbb {Z} ^{2}} ." Their results are termed the "Chayes–McKellar–Winn theorem". Later, when Chayes was asked to comment about the mathematical abilities
Danica_McKellar
Number divisible only by 1 and itself
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself
Prime_number
Book on the philosophy of mathematics
it can be separated out from the rest of the theory, according to Craig's theorem. However, Field rejected this approach to eliminating entities as uninformative
Science_Without_Numbers
Philosophy journal
2014. "Modes of Being and Quantification." Christian List. 1999. "Craig's Theorem and the Empirical Underdetermination Thesis Reassessed." Kevin Mulligan
Disputatio
Geometric relation between the roots of a polynomial and those of its derivative
In complex analysis, a branch of mathematics, the Gauss–Lucas theorem gives a geometric relation between the roots of a polynomial P and the roots of
Gauss–Lucas_theorem
Principle relating to fluid dynamics
that Bernoulli's theorem is responsible... Unfortunately, the 'dynamic lift' involved...is not properly explained by Bernoulli's theorem. a. Babinsky, Holger
Bernoulli's_principle
Mathematician and philosopher (1906–1978)
theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two
Kurt_Gödel
Graph of triangles with a shared vertex
combinatorial proof of the friendship theorem was given by Mertzios and Unger. Another proof was given by Craig Huneke. A formalised proof in Metamath
Friendship_graph
American statistician and academic (1924–2014)
Hogg and Craig (1956) for several interesting uses [of Basu's theorem] in proving results in distribution theory". The textbook "Hogg and Craig" was innovative
Robert_V._Hogg
Australian and American mathematician (born 1975)
and Sciences. Among his contributions to mathematics is the Green–Tao theorem on prime numbers, which he proved in 2004 in collaboration with Ben Green
Terence_Tao
About extensions of one-dimensional Noetherian rings (commutative algebra)
In commutative algebra, the Krull–Akizuki theorem states the following: Let A be a one-dimensional reduced noetherian ring, K its total ring of fractions
Krull–Akizuki_theorem
Ancient Greek mathematician (fl. 300 BC)
the later tradition of Alexandria. In the Elements, Euclid deduced the theorems from a small set of axioms. He also wrote works on perspective, conic sections
Euclid
Statistical principle
on an assumption of the distributional form (see Pitman–Koopman–Darmois theorem below), but remained very important in theoretical work. Roughly, given
Sufficient_statistic
On linear-time algorithms for graph logic
In the study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs
Courcelle's_theorem
Mathematical treatise by Euclid
These include the Pythagorean theorem, Thales' theorem, the Euclidean algorithm for greatest common divisors, Euclid's theorem that there are infinitely many
Euclid's_Elements
The only quadratic pairing functions are the Cantor polynomials
The Fueter–Pólya theorem, first proved by Rudolf Fueter and George Pólya, states that the only quadratic polynomial pairing functions are the Cantor polynomials
Fueter–Pólya_theorem
On domino tiling after removing two corners
dominoes; this result is Gomory's theorem, after mathematician Ralph E. Gomory, whose proof was published in 1973. Gomory's theorem can be proven using a Hamiltonian
Mutilated_chessboard_problem
Gives sufficient condition for Dehn filling to result in a negatively curved 3-manifold
In mathematics, the 2π theorem of Gromov and Thurston states a sufficient condition for Dehn filling on a cusped hyperbolic 3-manifold to result in a
2π_theorem
Statement in mathematical logic
(also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal
Diagonal_lemma
_{n\rightarrow \infty }{\frac {|\{1,2,\ldots ,n\}\cap A|}{n}}.} (Szemerédi's theorem) For any ultrafilter U {\displaystyle \mathbb {U} } on a set X {\displaystyle
Partition_regularity
Planar graph drawn by relaxing springs
the equations geometrically produces a planar embedding. Tutte's spring theorem, proven by W. T. Tutte (1963), states that this unique solution is always
Tutte_embedding
Theorem of mathematical logic
Robinson's joint consistency theorem is an important theorem of mathematical logic. It is related to Craig interpolation and Beth definability. The classical
Robinson's joint consistency theorem
Robinson's_joint_consistency_theorem
English actor (born 1967)
Boat, Classic Serial". BBC Radio 4. Retrieved 24 July 2016. "Birth of a Theorem, Book of the Week". BBC Radio 4. Retrieved 24 July 2016. "The Inheritor's
Julian_Rhind-Tutt
Principle suggesting that time travel paradoxes are inherently impossible
imposed by standard physical law. Similarly, physicist and astronomer J. Craig Wheeler concludes that: According to the consistency conjecture, any complex
Novikov self-consistency principle
Novikov_self-consistency_principle
Balanced complete multipartite graph
Erdős–Stone theorem extends Turán's theorem by bounding the number of edges in a graph that does not have a fixed Turán graph as a subgraph. Via this theorem, similar
Turán_graph
History Faculty at the University of Oxford 25 October 2012 Fermat's Last Theorem Marcus du Sautoy, Professor of Mathematics & Simonyi Professor for the
List of In Our Time programmes
List_of_In_Our_Time_programmes
American banker, businessman, investor, and amateur mathematician
for the Beal conjecture, a mathematical generalization of Fermat's Last Theorem. He has funded a $1 million standing prize for its proof or disproof. His
Andrew_Beal
Shape with three equal sides
the Reuleaux triangle Many theorems, inequalities, and problems involves equilateral triangles. For example, Napoleon's theorem stated that the centroid
Equilateral_triangle
Method of deriving conclusions
inferential steps and often use various rules of inference to establish the theorem they intend to demonstrate. Rules of inference are definitory rules—rules
Rule_of_inference
Three groups
explained in the MR review. It is known that F is not elementary amenable, see Theorem 4.10 in Cannon–Floyd–Parry. If F is not amenable, then it would be another
Thompson_groups
Mathematical representation
Squier's Form as Craig Squier was the first to explore its properties). Stephen Bigelow combined computer techniques and the Long–Paton theorem to show that
Burau_representation
theoretical physicist (Yang–Mills theory, Wu–Yang dictionary, Lee–Yang theorem), Nobel Prize laureate (1957). István Ágh, 87, Hungarian poet. Trevor Bentham
Deaths_in_October_2025
Probability puzzle
solution through a formal application of Bayes' theorem — among them books by Gill and Henze. Bayes' theorem states that the conditional probability that
Monty_Hall_problem
Motion of a curve based on its curvature
shortening on a sphere can be used as part of a proof of the tennis ball theorem. This theorem states that every smooth simple closed curve on the sphere that
Curve-shortening_flow
Tendency of AI systems to tell users what they want to hear
Jasper; Vechev, Martin (2025). "BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs". arXiv:2510.04721 [cs.LG]. Hong, Jisu; Byun, Jiyeon;
Sycophancy (artificial intelligence)
Sycophancy_(artificial_intelligence)
Category in mathematical category theory
Makkai, Michael (1 July 1995). "On Gabbay's Proof of the Craig Interpolation Theorem for Intuitionistic Predicate Logic". Notre Dame Journal of Formal
Coherent_category
Physical law for entropy and heat
proper definition of entropy and was based on caloric theory, is Carnot's theorem, formulated by the French scientist Sadi Carnot, who in 1824 showed that
Second_law_of_thermodynamics
Peter Lax, 99, Hungarian-born American mathematician (Lax equivalence theorem, Lax–Friedrichs method), Abel Prize laureate (2005), cardiac amyloidosis
Deaths_in_May_2025
American mathematician
of Michigan. He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence
Roger_Lyndon
Type of feedforward neural network
layers with a stride greater than one ignore the Nyquist–Shannon sampling theorem and might lead to aliasing of the input signal While, in principle, CNNs
Convolutional_neural_network
Relationship between programs and proofs
the type of values returned by a function) is analogous to a logical theorem, subject to hypotheses corresponding to the types of the argument values
Curry–Howard_correspondence
Branch of mathematical logic
without the cut rule. Gentzen's midsequent theorem, the Craig interpolation theorem, and Herbrand's theorem follow as corollaries of the cut-elimination
Proof_theory
2021) Duffin–Schaeffer theorem (Dimitris Koukoulopoulos, James Maynard, 2019) Main conjecture in Vinogradov's mean-value theorem (Jean Bourgain, Ciprian
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
American-born British filmmaker (born 1940)
Zero Theorem: Terry Gilliam's Latest!". Empire. 13 August 2012. Eisenberg, Eric (2012). "Christoph Waltz to Star in Terry Gilliam's Zero Theorem". Cinema
Terry_Gilliam
Branch of mathematics
nature of groups, with basic theorems such as the fundamental theorem of finite abelian groups and the Feit–Thompson theorem. The latter was a key early
Algebra
Quantum search algorithm
S2CID 258236417. Babbush, Ryan; McClean, Jarrod R.; Newman, Michael; Gidney, Craig; Boixo, Sergio; Neven, Hartmut (2021-03-29). "Focus beyond Quadratic Speedups
Grover's_algorithm
Nothing Bad Can Happen Our Heroes Died Tonight Patrick She Wolf The Zero Theorem U.S. premieres Afflicted Almost Human Blue Ruin Borgman Commando: A One
List of Fantastic Fest editions
List_of_Fantastic_Fest_editions
Book by Raymond Smullyan
computability and Gödel's theorem. While the book starts off with simple riddles, it eventually shifts to a tale of Inspector Craig of Scotland Yard, who
To_Mock_a_Mockingbird
Star at the centre of the Solar System
centre, releasing gravitational potential energy. According to the virial theorem, half of this released gravitational energy goes into heating, which leads
Sun
Climatic cooling after the Medieval Warm Period (16th–19th centuries)
field of the solar surface and solar atmosphere (corona). Because Alfvén's theorem applies, the coronal magnetic field is dragged out into the heliosphere
Little_Ice_Age
Array of numbers
III.2.1. Brown (1991), Theorem III.2.12. Brown (1991), Corollary III.2.16. Mirsky (1990), Theorem 1.4.1. Brown (1991), Theorem III.3.18. Eigen means "own"
Matrix_(mathematics)
Swiss mathematician (1707–1783)
properties of this function, he generalized Fermat's little theorem to what is now known as Euler's theorem. He contributed significantly to the theory of perfect
Leonhard_Euler
American voice actor (born 1962)
Episode: "Gone With the Wand" Transformers: Robots in Disguise Axiom and Theorem Episode: "Brainpower" New Looney Tunes Hubie and Bertie Episode: "Appropriate
Jeff_Bennett
only if they have the same multiplicity. Dedekind–Kummer theorem Swanson & Huneke 2006, Theorem 11.3.1 Eisenbud, David, Commutative Algebra with a View
Integral_closure_of_an_ideal
V. Club. Coates, Tyler (January 29, 2022). "Hollywood Flashback: Daniel Craig and Sam Mendes Bonded on 'Perdition' 20 Years Ago". The Hollywood Reporter
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
Branch of mathematics
Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th
Topology
Neoclassical economic model
The Lange model (or Lange–Lerner theorem) is a neoclassical economic model for a hypothetical socialist economy based on public ownership of the means
Lange_model
Argument for the existence of God
For scientific confirmation of premise 2, Craig refers to the Borde–Guth–Vilenkin theorem, a kinematic theorem that determines a past boundary to cosmic
Cosmological_argument
Class of partial differential equations
particular, the ultrahyperbolic equation satisfies an analog of the mean value theorem for harmonic functions. Ismael Herrera; George F. Pinder. "APPENDIX A PARTIAL
Ultrahyperbolic_equation
2013 film by Neill Blomkamp
Zero Theorem". Vulture. Retrieved May 2, 2023. Eisenberg, Eric (October 10, 2012). "Matt Damon Takes A Small Part In Terry Gilliam's The Zero Theorem". Cinema
Elysium_(film)
British actor (born 1981)
Friend was once again mentioned as the possible next James Bond when Daniel Craig gave up the role. He played a lead role in the 2021 horror film Separation
Rupert_Friend
Algebraic surface
The icosagon (of area 12 π {\displaystyle 12\pi } , by the Gauss-Bonnet theorem) can be tessellated by 240 (2,4,5) triangles. The actions that transport
Bring's_curve
Hypothetical travel into the past or future
or cosmic strings has been put forward by Stephen Hawking, who proved a theorem showing that according to general relativity it is impossible to build
Time_travel
Graph able to be embedded on a torus
Tutte's spring theorem applies in this case. Toroidal graphs also have book embeddings with at most 7 pages. By the Robertson–Seymour theorem, there exists
Toroidal_graph
Shape with four equal sides and angles
number of equal-area triangles, a result of Monsky's theorem. Cross's theorem or Vecten's theorem states that, for a triangle formed by the sides of three
Square
Proving validity without revealing other data
the amount of knowledge that must be communicated in order to prove a theorem. The quadratic nonresidue problem has both an NP and a co-NP algorithm
Zero-knowledge_proof
Argument that leads to a logical absurdity
derived a contradiction. Euclid's theorem states that there are infinitely many primes. In Euclid's Elements, the theorem is stated in Book IX, Proposition
Reductio_ad_absurdum
Australian scientist
until the advent of the Fluctuation Theorem. Crooks fluctuation theorem – an example of transient fluctuation theorem relating the dissipated work in nonequilibrium
Denis_Evans
Principle in AI development
model checking was the most common technique for agent verification, with theorem proving the second most commonly used formal verification method. In the
Agent_verification
Apologies: Portrait of a Problematic Vocation 2015 Cédric Villani Birth of a Theorem: A Mathematical Adventure 2015 Medicine Albert Schweitzer Out of My Life
List_of_autobiographies
Turkic ethnic group
component of 5G technologies. Mathematician Cahit Arf is known for Hasse–Arf theorem and Arf invariant. Physician Hulusi Behçet discovered Behçet's disease
Turkish_people
Computer hardware technology that uses quantum mechanics
be replaced with a finite gate set by appealing to the Solovay-Kitaev theorem. Implementation of Boolean functions using the few-qubit quantum gates
Quantum_computing
elementary embeddings ultraproducts, Los' theorem saturated models axiomatizability varieties, Birkhoff axiomatizability Craig interpolation Robinson consistency
Institutional_model_theory
Cryptographic primitive
Originally, non-interactive zero-knowledge was only defined as a single theorem-proof system. In such a system each proof requires its own fresh common
Non-interactive zero-knowledge proof
Non-interactive_zero-knowledge_proof
German logician and mathematician (1871–1953)
Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. Furthermore, his 1929 work on ranking chess players is the first description
Ernst_Zermelo
Ancient Greek philosopher (c. 428-347 BC)
examples for the Forms were the truths of geometry, such as the Pythagorean theorem. The theory of Forms is first introduced in the Phaedo dialogue (also known
Plato
Hungarian mathematician and operations researcher
frequently used due to its simplicity and rapid convergence. Kruskal's tree theorem states that, in every infinite set of finite trees, there exists a pair
Andrew_Vázsonyi
American mathematician and logician (1919–2017)
understanding of Gödel's theorem dates from this paper. Smullyan later made a compelling case that much of the fascination with Gödel's theorem should be directed
Raymond_Smullyan
Chinese-American physicist (Lee–Yang theory, Kinoshita–Lee–Nauenberg theorem, Lee–Yang theorem), Nobel Prize laureate (1957). Juan Ramón Martínez, 76, Salvadoran
Deaths_in_August_2024
American philosopher of science (born 1958)
book, Quantum Non-Locality and Relativity (1994), Maudlin explains Bell's Theorem and the tension between violations of Bell's inequality and relativity
Tim_Maudlin
history in commutative algebra. Krull's famous proof of his principal ideal theorem uses them in an essential way. They first arose after primary decompositions
Symbolic_power_of_an_ideal
German-American mathematician (1928–1999)
embedding which could be viewed as a borderline case of the Sobolev embedding theorem. Moser found the sharp constant in Trudinger's inequality, with the corresponding
Jürgen_Moser
Ambrosetti, 75, Italian mathematician, discoverer of the mountain pass theorem. Patricia Beatty, 84, Canadian choreographer and dancer. Jorge Horacio
Deaths_in_November_2020
Schmucker - (Nettmann) Simon Schwartz - Matthias Schultheiss - (Bell's Theorem) Axel Schumacher - (High Speed) Harald Siepermann - (Alfred Jodocus Kwak)
List_of_comics_creators
American science documentary television series
battling against the Frost giants with his hammer. Gödel's incompleteness theorems state that there is no system that can proves every assertion within itself
Through_the_Wormhole
Number measuring the chance an event occurs
incorporates all the information known to date. By Aumann's agreement theorem, Bayesian agents whose prior beliefs are similar will end up with similar
Probability
Topics referred to by the same term
make the transition to a knowledge-based economy Kolmogorov–Arnold–Moser theorem Komite-ye Amniyat-e Melli (National Security Committee), the forerunner
Kam_(disambiguation)
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