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Theorem in computability theory
Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. The statement of Post's theorem
Post's_theorem
Theorem that arithmetical truth cannot be defined in arithmetic
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations
Tarski's undefinability theorem
Tarski's_undefinability_theorem
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Theorem about Turing reductions
middle of the 1950s. It is a more general view of the Kleene–Post theorem. The Kleene–Post theorem states that there exist incomparable languages A and B that
Friedberg–Muchnik_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Hierarchy of complexity classes for formulas defining sets
Thus the hierarchy does not collapse. This is a direct consequence of Post's theorem. The inclusions Δ n 0 ⊊ Π n 0 {\displaystyle \Delta _{n}^{0}\subsetneq
Arithmetical_hierarchy
Set of all true first-order statements about the arithmetic of natural numbers
canonical Gödel number of the sentence θ. Post's theorem is a sharper version of the undefinability theorem that shows a relationship between the definability
True_arithmetic
Theorem in economics
Coase theorem (/ˈkoʊs/) postulates the economic efficiency of an economic allocation or outcome in the presence of externalities. The theorem is significant
Coase_theorem
American mathematician and logician (1897 – 1954)
to Gödel in 1938: I would have discovered Gödel's theorem in 1921—if I had been Gödel. In 1936, Post developed, independently of Alan Turing, a mathematical
Emil_Leon_Post
Study of computable functions and Turing degrees
precise by Post's theorem. A weaker relationship was demonstrated by Kurt Gödel in the proofs of his completeness theorem and incompleteness theorems. Gödel's
Computability_theory
Operation in computability theory
the problem X. That is, the problem X′ is not Turing-reducible to X. Post's theorem establishes a relationship between the Turing jump operator and the
Turing_jump
Theorem in physics
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with
Bell's_theorem
Principle in quantum information theory
In physics, the no-communication theorem (also referred to as the no-signaling principle) is a no-go theorem in quantum information theory. It asserts
No-communication_theorem
Theorem in quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement
No-cloning_theorem
Theorem in electrical circuit analysis
stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "Any linear electrical network containing only voltage sources
Thévenin's_theorem
Plurality voting system
First-past-the-post (FPTP) — also called choose-one, first-preference plurality (FPP), or simply plurality — is a single-winner voting rule. Each voter
First-past-the-post_voting
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
Theorem in game theory
Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if
Aumann's_agreement_theorem
Counterintuitive result in probability
The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will
Infinite_monkey_theorem
Branch of mathematical logic
are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast
Reverse_mathematics
Theorem relating continuity to graphs
closed graphs are necessarily continuous. A blog post by T. Tao lists several closed graph theorems throughout mathematics. If f : X → Y {\displaystyle
Closed_graph_theorem
Condition under which an odd prime is a sum of two squares
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p = x 2 + y 2 , {\displaystyle p=x^{2}+y^{2}
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Type of number sequence
is countable, so f is zero almost everywhere. In fact, the de Bruijn–Post Theorem states the converse of the above criterion: If f is a function such that
Equidistributed_sequence
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
Formal language
context-sensitive and recursive languages are recursively enumerable. Post's theorem shows that RE, together with its complement co-RE, correspond to the
Recursively enumerable language
Recursively_enumerable_language
Measure of unsolvability
an infinite sequence ai of degrees such that a′i+1 ≤ ai for each i. Post's theorem establishes a close correspondence between the arithmetical hierarchy
Turing_degree
Black holes are characterized only by mass, charge, and spin
The no-hair theorem, also known as the black hole uniqueness theorem, states that all stationary black hole solutions of the Einstein–Maxwell equations
No-hair_theorem
Theorem pertaining to the ontology of quantum mechanics
Pusey–Barrett–Rudolph (PBR) theorem is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named)
Pusey–Barrett–Rudolph_theorem
American philosopher and logician (1940–2022)
application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable
Saul_Kripke
Key results in general relativity on gravitational singularities
when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Theorem on operator interpolation
analysis, the Riesz–Thorin theorem, often referred to as the Riesz–Thorin interpolation theorem or the Riesz–Thorin convexity theorem, is a result about interpolation
Riesz–Thorin_theorem
In algebra, the first and second fundamental theorems of invariant theory concern the generators and relations of the ring of invariants in the ring of
First and second fundamental theorems of invariant theory
First_and_second_fundamental_theorems_of_invariant_theory
Mathematical theorem
In real analysis, a branch of mathematics, Bernstein's theorem, named after Sergei Bernstein, states that every real-valued function on the half-line
Bernstein's theorem on monotone functions
Bernstein's_theorem_on_monotone_functions
Theorem of quantum information theory
The no-hiding theorem states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot
No-hiding_theorem
Automated theorem proving ACL2 theorem prover E equational theorem prover Gandalf theorem prover HOL theorem prover Isabelle theorem prover LCF theorem prover
List of mathematical logic topics
List_of_mathematical_logic_topics
recherche en informatique fondamentale. Retrieved 2025-10-07. Kleene's theorem is usually considered as the starting point of automata theory. Kahrs,
List of pioneers in computer science
List_of_pioneers_in_computer_science
Overview of and topical guide to logic
Cantor's theorem Church's theorem Church's thesis Effective method Formal system Gödel's completeness theorem Gödel's first incompleteness theorem Gödel's
Outline_of_logic
Theorem in statistical mathematics
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently
Fluctuation_theorem
Concept in computability theory
the results of the computation if the program does halt. As with the smn theorem, the original notation used by Kleene has become standard terminology for
Kleene's_T_predicate
Statement of spherically symmetric spacetimes
In general relativity, Birkhoff–Jebsen's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically
Birkhoff's theorem (relativity)
Birkhoff's_theorem_(relativity)
Method of comparing problems by transforming one into another in computability theory
extra predicate for B {\displaystyle B} . Equivalently, according to Post's theorem, A is arithmetical in B {\displaystyle B} if and only if A {\displaystyle
Reduction (computability theory)
Reduction_(computability_theory)
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
Problem in computer science
Minsky notes: ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram
Halting_problem
British mathematician who proved Fermat's Last Theorem
specialising in number theory. He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016 Abel Prize and the 2017 Copley Medal
Andrew_Wiles
Theorem in theoretical computer science
database theory, the PACELC design principle is an extension to the CAP theorem. It states that in case of network partitioning (P) in a distributed computer
PACELC_design_principle
American actress, mathematics writer, and education advocate (born 1975)
(August 20, 2007). "Blog post by mathematician, and a former instructor of McKellar's, complimenting her book and explaining the theorem". Chang, Kenneth (July
Danica_McKellar
Limit of a uniformly computable sequence of functions
_{2}^{0}} sets are just the sets computable from 0 ′ {\displaystyle 0'} by Post's theorem, the limit lemma also entails that the limit computable sets are the
Computation_in_the_limit
Fundamental combinatorial result of Ramsey theory
In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory, named after Alfred W. Hales and Robert I. Jewett, that
Hales–Jewett_theorem
Russian mathematician (born 1966)
Polikanova, he established a measure-theoretic formulation of Helly's theorem.[PP86] In 1987, the year he began graduate studies, he published an article
Grigori_Perelman
In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation
Weyl's theorem on complete reducibility
Weyl's_theorem_on_complete_reducibility
Hungarian and American mathematician and physicist (1903–1957)
the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter unitary groups t → V t {\displaystyle
John_von_Neumann
Any individual whose preferences satisfy four axioms has a utility function
In decision theory, the von Neumann–Morgenstern (VNM) utility theorem demonstrates that rational choice under uncertainty involves making decisions that
Von Neumann–Morgenstern utility theorem
Von_Neumann–Morgenstern_utility_theorem
Economic theorem
The Sonnenschein–Mantel–Debreu theorem is an important result in general equilibrium economics, proved by Gérard Debreu, Rolf Mantel [es], and Hugo F
Sonnenschein–Mantel–Debreu theorem
Sonnenschein–Mantel–Debreu_theorem
Theorem of quantum information processing
no-broadcasting theorem is a result of quantum information theory. In the case of pure quantum states, it is a corollary of the no-cloning theorem. The no-cloning
No-broadcasting_theorem
Theorem in geometric topology
conjecture (UK: /ˈpwæ̃kæreɪ/, US: /ˌpwæ̃kɑːˈreɪ/, French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds
Poincaré_conjecture
Quantum error correction schemes can suppress the logical error rate arbitrarily low
In quantum computing, the threshold theorem (or quantum fault-tolerance theorem) states that a quantum computer with a physical error rate below a certain
Threshold_theorem
Theorem in theoretical physics
In theoretical physics, the Haag–Łopuszański–Sohnius theorem states that if both commutating and anticommutating generators are considered, then the only
Haag–Łopuszański–Sohnius theorem
Haag–Łopuszański–Sohnius_theorem
Field of knowledge
and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems
Mathematics
The 2D Z-transform, similar to the Z-transform, is used in multidimensional signal processing to relate a two-dimensional discrete-time signal to the complex
2D_Z-transform
Number in {..., –2, –1, 0, 1, 2, ...}
products of primes in an essentially unique way. This is the fundamental theorem of arithmetic. Z {\displaystyle \mathbb {Z} } is a totally ordered
Integer
Establish relationships between homology and cohomology theories
In algebraic topology, universal coefficient theorems establish relationships between homology groups (or cohomology groups) with different coefficients
Universal_coefficient_theorem
On the approximate structure of sets whose sumset is small
In additive combinatorics, a discipline within mathematics, Freiman's theorem is a central result which indicates the approximate structure of sets whose
Freiman's_theorem
universal fostering of social equality was an overriding priority. The post-Mao Zedong Chinese Communist Party leadership views education as the foundation
Education_in_China
Economic theorem
The Henry George theorem (HGT) states that under certain conditions, aggregate spending by government on public goods will increase aggregate rent based
Henry_George_theorem
Theorem that the sum of the reciprocals of the twin primes converges
In number theory, Brun's theorem states that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a finite
Brun's_theorem
Formal semantics for non-classical logic systems
application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable
Kripke_semantics
Impossible task in computing
impossible by Alonzo Church and Alan Turing in 1936. By the completeness theorem of first-order logic, a statement is universally valid if and only if it
Entscheidungsproblem
Theorem in group theory
mathematical subject of group theory, the Grushko theorem or the Grushko–Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality
Grushko_theorem
Country in South Asia
BCE) contain the earliest extant verbal expression of the Pythagorean theorem (although very likely it had been known to the Old Babylonians.) All mathematical
India
Method by which voters make a choice between options
including Arrow's impossibility theorem (showing that ranked voting cannot eliminate the spoiler effect) and Gibbard's theorem (showing it is impossible to
Electoral_system
Japanese mathematician
known for the Hille-Yosida theorem concerning C0-semigroups. Yosida studied mathematics at the University of Tokyo, and held posts at Osaka and Nagoya Universities
Kōsaku_Yosida
Voting systems that use ranked ballots
first-past-the-post voting. Rated voting systems produce more information than ordinal ballots; as a result, some common results like Arrow's theorem do not directly
Ranked_voting
Intelligence of machines
Nilsson (1998, chpt. 3.3) Universal approximation theorem: Russell & Norvig (2021, p. 752) The theorem: Cybenko (1988), Hornik, Stinchcombe & White (1989)
Artificial_intelligence
American columnist, author and lecturer (born 1946)
Last Theorem, Savant published the book The World's Most Famous Math Problem (October 1993), which surveys the history of Fermat's Last Theorem as well
Marilyn_vos_Savant
English theoretical physicist (1942–2018)
included a collaboration with Roger Penrose on gravitational singularity theorems in the framework of general relativity, and the theoretical prediction
Stephen_Hawking
Foundational theorem of quantum information processing
In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary
No-deleting_theorem
1968 film by Pier Paolo Pasolini
Teorema (English: "Theorem") is a 1968 Italian allegorical art film written and directed by Pier Paolo Pasolini. The film centers on an upper-class Milanese
Teorema
Theorem in general relativity
Lovelock's theorem of general relativity says that from a local gravitational action which contains only second derivatives of the four-dimensional spacetime
Lovelock's_theorem
American-born British mathematician (1888-1972)
also built up the department, offering posts to a number of outstanding mathematicians who had been forced from posts on the continent of Europe. He brought
Louis_J._Mordell
1995 US criminal trial
disclosed the hoax. The trial provided an example of incorrect use of Bayes theorem in the courtroom that is used in statistics courses around the world. O
Murder_trial_of_O._J._Simpson
Canadian cryptographer (born c. 1970)
also at the University of Oxford. In the field of cryptography, Mosca's theorem addresses the question of how soon an organization needs to act in order
Michele_Mosca
1995 film by Terry Gilliam
Theorem in 2013, claims were made that Gilliam had meant it as part of a trilogy. A 2013 review for The Guardian said, "Calling it [The Zero Theorem]
12_Monkeys
Indian mathematician (1887–1920)
notes, Hardy commented that Ramanujan had produced groundbreaking new theorems, including some that "defeated me completely; I had never seen anything
Srinivasa_Ramanujan
Mathematical result on arithmetic properties of binomial coefficients
The Star of David theorem is a mathematical result on arithmetic properties of binomial coefficients. It was discovered by Henry W. Gould in 1972. The
Star_of_David_theorem
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
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
Cryptography secured against quantum computers
current algorithms will be vulnerable to quantum computing attacks. Mosca's theorem provides the risk analysis framework that helps organizations identify
Post-quantum_cryptography
Bound on the number of incidences between points and lines in the plane
The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given n points and m lines in the Euclidean
Szemerédi–Trotter_theorem
Economic model for international trade
Stolper–Samuelson theorem). The Magnification effect on production quantity-shifts induced by endowment changes (via the Rybczynski theorem) predicts a larger
Heckscher–Ohlin_model
Theorem stating the impossibility of converting qubits into bits
In quantum information theory, the no-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence of classical bits
No-teleportation_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
Election that narrows the field of candidates before an election for office
spectrum. In the general election, under the assumptions of the median voter theorem, the candidate must move more towards the center in hopes of capturing
Primary_election
Compact astronomical body
physicists to produce a body of work that became known as the no-hair theorem, which states that a stationary black hole is completely described by the
Black_hole
Algorithm for public-key cryptography
λ(pq)). This is part of the Chinese remainder theorem, although it is not the significant part of that theorem. Although the original paper of Rivest, Shamir
RSA_cryptosystem
On smallest surface enclosing two volumes
In the mathematical theory of minimal surfaces, the double bubble theorem states that the shape that encloses and separates two given volumes and has
Double_bubble_theorem
Computational quantum mechanical modelling method to investigate electronic structure
Pierre Hohenberg in the framework of the two Hohenberg–Kohn theorems (HK). The original HK theorems held only for non-degenerate ground states in the absence
Density_functional_theory
French mathematician, physicist and engineer (1854–1912)
theory. He famously introduced the concept of the Poincaré recurrence theorem, which states that a state will eventually return arbitrarily close to
Henri_Poincaré
British mathematician
bounds. In 1998, Gowers proved the first effective bounds for Szemerédi's theorem, showing that any subset A ⊂ { 1 , … , N } {\displaystyle A\subset \{1
Timothy_Gowers
Weakly optimal allocation of resources
per the Greenwald–Stiglitz theorem. The second welfare theorem is essentially the reverse of the first welfare theorem. It states that under similar
Pareto_efficiency
POSTS THEOREM
POSTS THEOREM
Boy/Male
Muslim
Pillar, Post, Support
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord of Poets; Lord Ganesha
Boy/Male
Indian
Pillar, Post, Support
Boy/Male
Indian
Pillar, Post, Support
Surname or Lastname
English and Scottish
English and Scottish : patronymic from Pott 1, particularly common in northeastern England.
Girl/Female
Tamil
One who poses all best qualities
Boy/Male
Indian, Sanskrit
Moon of Poets
Girl/Female
Hindu, Indian, Marathi
Post; Pillar; A Goddess
Boy/Male
Indian, Sanskrit
Lord of Poets
Girl/Female
Greek
Favorite name with poets.
Boy/Male
African, Arabic, Muslim, Swahili
Support; Pillar; Post
Boy/Male
Tamil
King of poets, Name of Lord Ganesh
Girl/Female
Hindu
One who poses all best qualities
Girl/Female
Biblical
The posts of a door, splendor, beauty.
Boy/Male
Muslim
Pillar, Post, Support
Boy/Male
Indian, Sanskrit
Lord of Poets
Boy/Male
Indian, Tamil
King of Poets
Boy/Male
Biblical
Lord of hosts.
Girl/Female
Tamil
Lord of poets, Lord Ganesh, Small poem
Biblical
the posts of a door; splendor; beauty
POSTS THEOREM
POSTS THEOREM
Girl/Female
Indian, Sanskrit
Divine Wine
Female
Egyptian
, goddess of the sunbeam; consort of Khnum.
Boy/Male
Tamil
Happy
Girl/Female
Assamese, Christian, Danish, Finnish, German, Gujarati, Hebrew, Hindu, Indian, Kannada, Malayalam, Marathi, Rajasthani, Swedish, Tamil, Telugu
The Earth
Boy/Male
American, British, Christian, Danish, Dutch, English, Finnish, French, German, Hawaiian, Hebrew, Hindu, Indian, Latin, Swedish, Swiss, Tamil, Zimbabwe
God is with Me
Boy/Male
Hindu
Auspicious
Girl/Female
Hindu
Name of Lord Murugan, Goddess Saraswati (Goddess of education
Girl/Female
Indian, Telugu
Having Fame
Boy/Male
Tamil
Soul, Life force
Boy/Male
Tamil
Lord Vishnu
POSTS THEOREM
POSTS THEOREM
POSTS THEOREM
POSTS THEOREM
POSTS THEOREM
v. t.
To attach to a post, a wall, or other usual place of affixing public notices; to placard; as, to post a notice; to post playbills.
v. t.
To carry, as an account, from the journal to the ledger; as, to post an account; to transfer, as accounts, to the ledger.
n.
A station, office, or position of service, trust, or emolument; as, the post of duty; the post of danger.
n.
One of two suspending posts in a roof truss, or other framed truss of similar form. See King-post.
adv.
With post horses; hence, in haste; as, to travel post.
n.
An established conveyance for letters from one place or station to another; especially, the governmental system in any country for carrying and distributing letters and parcels; the post office; the mail; hence, the carriage by which the mail is transported.
n.
See under 4th Post.
n.
A piece of timber, metal, or other solid substance, fixed, or to be fixed, firmly in an upright position, especially when intended as a stay or support to something else; a pillar; as, a hitching post; a fence post; the posts of a house.
v. t.
To assign to a station; to set; to place; as, to post a sentinel.
n.
A post-temporal bone.
v. i.
To travel with post horses; figuratively, to travel in haste.
n.
Same as King-post.
a.
After death; as, post-mortem rigidity.
v. t.
To hold up to public blame or reproach; to advertise opprobriously; to denounce by public proclamation; as, to post one for cowardice.
n.
A post (generally a pillar of iron) supporting a lamp or lantern for lighting a street, park, etc.
n.
One who posts bills; a billposter.
v. t.
To place in the care of the post; to mail; as, to post a letter.
n.
A station, or one of a series of stations, established for the refreshment and accommodation of travelers on some recognized route; as, a stage or railway post.