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The Complete class theorems is a class of theorems in decision theory. They establish that all admissible decision rules are equivalent to the Bayesian
Complete_class_theorem
Statistics term
models have a sufficient statistic which is not complete. This is important because the Lehmann–Scheffé theorem cannot be applied to such models. Galili and
Completeness_(statistics)
Fundamental theorem in mathematical logic
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability
Gödel's_completeness_theorem
Middle quantile of a data set or probability distribution
187–193. Brown, L. D.; Cohen, Arthur; Strawderman, W. E. (1976). "A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications". Ann. Statist
Median
Complexity class
smaller class than polynomial-time reductions. The concept of NP-completeness was introduced in 1971 (see Cook–Levin theorem), though the term NP-complete was
NP-completeness
Limitative results in mathematical logic
and in philosophy of mathematics. The theorems are interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete. That is, it is in NP, and
Cook–Levin_theorem
The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an
Original proof of Gödel's completeness theorem
Original_proof_of_Gödel's_completeness_theorem
Impossible task in computing
to be 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
Entscheidungsproblem
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
Class in computational complexity theory
denotes the class of languages recognizable by a family of branching programs of bounded width and polynomial length. Barrington's theorem says that BWBP
NC_(complexity)
Statement in mathematical combinatorics
large complete graph. As the simplest example, consider two colours (say, blue and red). Let r and s be any two positive integers. Ramsey's theorem states
Ramsey's_theorem
Result about when a matrix can be diagonalized
operators on infinite-dimensional spaces. In general, the spectral theorem identifies a class of linear operators that can be modeled by multiplication operators
Spectral_theorem
In mathematics, a statement that has been proven
mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
Describes the objects of a given type, up to some equivalence
only classifies every class, but provides a distinguished (canonical) element of each class. There exist many classification theorems in mathematics, as
Classification_theorem
Statistical property
1214/aos/1176344563. Brown, L. D.; Cohen, Arthur; Strawderman, W. E. (1976). "A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications". Ann. Statist
Bias_of_an_estimator
Complexity class used to classify decision problems
would exist for solving NP-complete, and by corollary, all NP problems. The complexity class NP is related to the complexity class co-NP, for which the answer
NP_(complexity)
When a finite set S of relations yields polynomial-time or NP-complete problems
or is NP-complete, as opposed to one of the classes of intermediate complexity that is known to exist (assuming P ≠ NP) by Ladner's theorem. Special cases
Schaefer's_dichotomy_theorem
Sufficiency theorem for reconstructing signals from samples
reconstructed exactly from those samples. Strictly speaking, the theorem only applies to a class of mathematical functions having a Fourier transform that is
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Theorem in stochastic calculus
proved such a theorem, which became known as the Doob-Meyer decomposition. In honor of Doob, Meyer used the term "class D" to refer to the class of supermartingales
Doob–Meyer decomposition theorem
Doob–Meyer_decomposition_theorem
Subfield of automated reasoning and mathematical logic
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving
Automated_theorem_proving
Area of mathematical logic
stability spectrum theorem, which implies that every complete theory T in a countable signature falls in one of the following classes: There are no cardinals
Model_theory
1995 publication in mathematics
Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Graph that can be embedded in the plane
Kuratowski's theorem: A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of the complete graph K5 or the complete bipartite
Planar_graph
Concept in mathematical logic
\lor \}} is also functionally complete. (Its functional completeness is also proved by the Disjunctive Normal Form Theorem.) But this is still not minimal
Functional_completeness
Characteristic of some logical systems
called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise
Completeness_(logic)
Group of mathematical theorems
specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients
Isomorphism_theorems
theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order logic on the class of all finite models is
Trakhtenbrot's_theorem
Metric geometry
are complete are called geodesic manifolds; completeness follows from the Hopf–Rinow theorem. Every compact metric space is complete, though complete spaces
Complete_metric_space
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
Ability of a computing system to simulate Turing machines
items of an existing array). However, another theorem shows that there are problems solvable by Turing-complete languages that cannot be solved by any language
Turing_completeness
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
In board games that cannot end in a draw, one of the two players has a winning strategy
example game of chess in 1913. Zermelo's theorem can be applied to all finite-stage two-player games with complete information and alternating moves. The
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Theorem in computability theory
In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about
Rice's_theorem
Topics referred to by the same term
Gödel's completeness theorem, correspondence between semantic truth and syntactic provability in first-order logic Gödel's incompleteness theorems, limits
Completeness
Gives necessary and sufficient conditions for two braids to have equivalent closures
In mathematics the Markov theorem gives necessary and sufficient conditions for two braids to have closures that are equivalent knots or links. The conditions
Markov_theorem
Every finite abelian extension of Q is contained within some cyclotomic field
a fact generalised in class field theory. The theorem was first stated by Kronecker (1853) though his argument was not complete for extensions of degree
Kronecker–Weber_theorem
Mathematical proposition equivalent to the axiom of choice
the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space
Zorn's_lemma
Unsolved problem in computer science
Kurt Gödel to John von Neumann, Gödel asked whether theorem-proving (now known to be co-NP-complete) could be solved in quadratic or linear time, and posited
P_versus_NP_problem
Partially ordered set in which all subsets have both a supremum and infimum
them as a special class of lattices. Complete lattices must not be confused with complete partial orders (CPOs), a more general class of partially ordered
Complete_lattice
On coloring the edges of graphs
In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than
Vizing's_theorem
Computation modulo a fixed integer
important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special
Modular_arithmetic
Class of algebraic structures
abelian groups, the rings, the monoids etc. According to Birkhoff's theorem, a class of algebraic structures of the same signature is a variety if and only
Variety_(universal_algebra)
Branch of applied probability theory
can arise from departures from the probability axioms, and the complete class theorems, which show that all admissible decision rules are equivalent to
Decision_theory
Algorithmic complexity class
space complexity classes in the following way: P ⊆ NP ⊆ PSPACE ⊆ EXPTIME ⊆ NEXPTIME ⊆ EXPSPACE. Furthermore, by the time hierarchy theorem and the space
EXPTIME
Branch of mathematical combinatorics
dimensions. The Hales–Jewett theorem implies Van der Waerden's theorem. A theorem similar to van der Waerden's theorem is Schur's theorem: for any given c there
Ramsey_theory
Every Riemannian manifold can be isometrically embedded into some Euclidean space
The first theorem is for continuously differentiable (C1) embeddings and the second for embeddings that are analytic or smooth of class Ck, 3 ≤ k ≤
Nash_embedding_theorems
Set of sentences in a formal language
first-order logic, the most important case, it follows from the completeness theorem that the two meanings coincide. In other logics, such as second-order
Theory_(mathematical_logic)
Quadratic imaginary number fields with unique factorisation
In number theory, the Heegner theorem or Stark-Heegner theorem establishes the complete list of the quadratic imaginary number fields whose rings of integers
Stark–Heegner_theorem
Non-contradiction of a theory
and complete. Gödel's incompleteness theorems show that any sufficiently strong recursively enumerable theory of arithmetic cannot be both complete and
Consistency
Problem in computer science
statement of the incompleteness theorem by asserting that an effective axiomatization of the natural numbers that is both complete and sound is impossible. The
Halting_problem
Condition for a linear operator to be open
category theorem, and completeness of both E {\displaystyle E} and F {\displaystyle F} is essential to the theorem. The statement of the theorem is no longer
Open mapping theorem (functional analysis)
Open_mapping_theorem_(functional_analysis)
On graph coloring and neighborhood size
colors, except for two cases, complete graphs and cycle graphs of odd length, which require Δ + 1 colors. The theorem is named after R. Leonard Brooks
Brooks'_theorem
Theorem for proving more complex theorems
also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however
Lemma_(mathematics)
Due to the concise yet complete description of many dynamical systems, Conley's theorem is also known as the fundamental theorem of dynamical systems.
Conley's fundamental theorem of dynamical systems
Conley's_fundamental_theorem_of_dynamical_systems
Completes the Langlands program for general linear groups over algebraic function fields
In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields
Lafforgue's_theorem
structure theorem, introduced by Cohen (1946), describes the structure of complete Noetherian local rings. Some consequences of Cohen's structure theorem include
Cohen_structure_theorem
Gives sufficient condition for Dehn filling to result in a negatively curved 3-manifold
the isotopy class. The 2π theorem states: a Dehn filling of M with each filling slope greater than 2π results in a 3-manifold with a complete metric of
2π_theorem
Existence and uniqueness of solutions to initial value problems
known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard,
Picard–Lindelöf_theorem
Undecidability of equality of real numbers
Richardson of the University of Bath. Specifically, the class of expressions for which the theorem holds is that generated by rational numbers, the number
Richardson's_theorem
System of mathematical set theory
quantifiers range over classes. NBG is finitely axiomatizable, while ZFC and MK are not. A key theorem of NBG is the class existence theorem, which states that
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
On collapse of the polynomial hierarchy if NP is in non-uniform polynomial time class
(Adleman's theorem), the theorem is also evidence that the use of randomization does not lead to polynomial time algorithms for NP-complete problems. The
Karp–Lipton_theorem
Statistical property
1214/aos/1176344563. Brown, L.D.; Cohen, Arthur; Strawderman, W.E. (1976). "A complete class theorem for strict monotone likelihood ratio with applications". Annals
Monotone_likelihood_ratio
Existence and cardinality of models of logical theories
In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf
Löwenheim–Skolem_theorem
Category of mathematical proof
In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as
Proof_of_impossibility
Basic result in harmonic analysis on compact topological groups
In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are
Peter–Weyl_theorem
Visual depiction of a partially ordered set
& Tamassia (1995a), Theorem 9, p. 118; Baker, Fishburn & Roberts (1971), theorem 4.1, page 18. Garg & Tamassia (1995a), Theorem 15, p. 125; Bertolazzi
Hasse_diagram
Axiom of set theory
orthonormal basis. The Banach–Alaoglu theorem about compactness of sets of functionals. The Baire category theorem about complete metric spaces, and its consequences
Axiom_of_choice
Theorem about metric spaces
Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important
Banach_fixed-point_theorem
Theorem in mathematics
"nonzero Jacobian determinant". If the function of the theorem belongs to a higher differentiability class, the same is true for the inverse function. There
Inverse_function_theorem
Class of theorems about Nash equilibrium payoff profiles in repeated games
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The
Folk_theorem_(game_theory)
Finiteness of sets of forbidden graph minors
Wagner's theorem characterizes the planar graphs as being the graphs that do not have the complete graph K 5 {\displaystyle K_{5}} or the complete bipartite
Robertson–Seymour_theorem
On forbidden subgraphs in planar graphs
In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states
Kuratowski's_theorem
Paradox in set theory
145–159; reprinted in Quine 1955b: Appendix. Completeness of quantification theory. Loewenheim's theorem, enclosed as a pamphlet with part of the third
Russell's_paradox
Perfect graphs have neither odd holes nor odd antiholes
In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither
Strong_perfect_graph_theorem
Index of articles associated with the same name
sign with an inequality sign, form a broad class of such auxiliary relations. One instance of such theorem was used by Aronson and Weinberger to characterize
Comparison_theorem
Generalizes the Kodaira vanishing theorem
of holomorphic (p,0)-forms taking values on F. The theorem states that, if the first Chern class of F is negative, H q ( M ; Ω p ( F ) ) = 0 when q
Nakano_vanishing_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
Ideals in a Boolean algebra can be extended to prime ideals
In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement
Boolean_prime_ideal_theorem
Type of theory in mathematical logic
categoricity theorem (1965) confirms that these are the only possibilities: Morley's categoricity theorem (Morley 1965)—If T is a consistent and complete theory
Categorical_theory
Study of computable functions and Turing degrees
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
On chains and antichains in partial orders
mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an
Dilworth's_theorem
Form of mathematical proof
1000 AD, who applied it to arithmetic sequences to prove the binomial theorem and properties of Pascal's triangle. Whilst the original work was lost
Mathematical_induction
Mathematical-logic system based on functions
– A virtual machine designed for the lambda calculus Scott–Curry theorem – A theorem about sets of lambda terms To Mock a Mockingbird – An introduction
Lambda_calculus
Concept in model theory
that every model realizes p (at least if the theory is complete). The omitting types theorem says that conversely if p is not isolated then there is
Type_(model_theory)
Form of logic that allows quantification over predicates
used in the context of Courcelle's theorem, an algorithmic meta-theorem in graph theory. The MSO theory of the complete infinite binary tree (S2S) is decidable
Second-order_logic
Theorem classifying finite simple groups
enormous theorem) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called
Classification of finite simple groups
Classification_of_finite_simple_groups
Mathematical construction
include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization
Ultraproduct
Mathematical theorem
In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was
Riemann–Roch theorem for surfaces
Riemann–Roch_theorem_for_surfaces
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
In combinatorics
In mathematics, the Graham–Rothschild theorem is a theorem that applies Ramsey theory to combinatorics on words and combinatorial cubes. It is named after
Graham–Rothschild_theorem
Logic statement about a formal system proven in a metalanguage
is a class consisting of the sets satisfying the formula. Consistency proofs of systems such as Peano arithmetic. Gödel's completeness theorem states
Metatheorem
Every set is smaller than its power set
elegant and remarkably simple. The complete proof is presented below, with detailed explanations to follow. Theorem (Cantor)—Let f {\displaystyle f} be
Cantor's_theorem
Type of "good" decision rule in Bayesian statistics
possible to define a generalized Bayes rule. According to the complete class theorems, under mild conditions every admissible rule is a (generalized)
Admissible_decision_rule
Standard system of axiomatic set theory
sense that any theorem not mentioning classes and provable in one theory can be proved in the other. Gödel's second incompleteness theorem says that a recursively
Zermelo–Fraenkel_set_theory
Logical principle
(see Nouveaux Essais, IV,2)" (ibid p 421) The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica
Law_of_excluded_middle
analysis and the sequential probability ratio test and on Wald's complete class theorem characterizing admissible decision rules as limits of Bayesian procedures
List of publications in statistics
List_of_publications_in_statistics
Basic framework of mathematics
generating self-contradictory theories, and to have reliable concepts of theorems, proofs, algorithms, etc. in particular. This may also include the philosophical
Foundations_of_mathematics
Existence of values making formula true
to consistency for first-order logic, a result known as Gödel's completeness theorem. The negation of satisfiability is unsatisfiability, and the negation
Satisfiability
Measure of algorithmic complexity
universal up to this additive constant. Theorem: If K1 and K2 are the complexity functions relative to Turing complete description languages L1 and L2, then
Kolmogorov_complexity
COMPLETE CLASS-THEOREM
COMPLETE CLASS-THEOREM
Girl/Female
Indian
Glass
Boy/Male
Australian, Danish, Dutch, Greek, Swedish
People of Victory; Victory of the People
Boy/Male
Arabic
Peace Maker; Brightness; Class
Surname or Lastname
English and German
English and German : metonymic occupational name for a glazier or glass blower, from Old English glæs ‘glass’ (akin to Glad, referring originally to the bright shine of the material), Middle High German glas.Irish and Scottish : Anglicized form of the epithet glas ‘gray’, ‘green’, ‘blue’ or any of various Gaelic surnames derived from it.German : altered form of the personal name Klass, a reduced form of Nikolaus (see Nicholas).Jewish (Ashkenazic) : ornamental name from German Glass ‘glass’, or a metonymic occupational name for a glazier or glass blower.
Girl/Female
Muslim
Glass
Boy/Male
Australian, Dutch, German, Greek
People's Victory
Surname or Lastname
English
English : from the medieval female personal name Cass, a short form of Cassandra. This was the name (of uncertain, possibly non-Greek, origin) of an ill-fated Trojan prophetess of classical legend, condemned to foretell the future but never be believed; her story was well known and widely popular in medieval England.
Surname or Lastname
English
English : variant of Close 1.German : variant of Kloss.
Girl/Female
Australian, French, Greek
Victory of the People
Surname or Lastname
English
English : nickname from Old French, Middle English cras ‘big’, ‘fat’ (Latin crassus).Possibly an altered spelling of German Krass.
Surname or Lastname
North German
North German : topographic name from Middle Low German plas ‘place’, ‘open square’, ‘street’.South German (also Pläss) : from a short form of the medieval personal name Blasius.English : variant of Place 3.
Surname or Lastname
North German variant of Laas 2.Jewish (Ashkenazic)
North German variant of Laas 2.Jewish (Ashkenazic) : unexplained.English : nickname from Middle English lesse, lasse ‘smaller’ (from Old English lǣssa ‘less’), perhaps also used in the sense ‘younger’.
Surname or Lastname
English
English : from the medieval personal name Classe, a short form of Nicholas. See also Clayson.Variant of Klaas or Klass, North German forms of Claus.
Boy/Male
English Latin Irish Welsh
Wealthy man.
Girl/Female
Indian
Glass
Girl/Female
Tamil
Glass
Male
German
Short form of German Niclaus, CLAUS means "victor of the people."Â
Girl/Female
Muslim/Islamic
Glass
Boy/Male
Greek Latin
People's victory.
Female
English
English short form of Latin Cassandra, CASS means "she who entangles men."Â
COMPLETE CLASS-THEOREM
COMPLETE CLASS-THEOREM
Boy/Male
Hindu, Indian, Kannada, Tamil, Telugu
Ocean; Sea
Boy/Male
Greek Latin
A river god.
Girl/Female
Indian
Charitable.
Girl/Female
Tamil
State of deathlessness, Immortality, Divine nectar of the gods
Boy/Male
Arabic, Muslim
Help; Support
Boy/Male
Bengali, Indian
Lightening Insect; Who is in Zone
Male
Egyptian
, a priest of Amen Ra.
Girl/Female
Tamil
Sthuthibhi | ஸà¯à®¤à¯à®¤à¯€à®ªà¯€
With prayers
Biblical
a redeemer; redeemed; defiled
Boy/Male
Bengali, Gujarati, Hindu, Indian, Malayalam, Marathi, Telugu
Eye of the World
COMPLETE CLASS-THEOREM
COMPLETE CLASS-THEOREM
COMPLETE CLASS-THEOREM
COMPLETE CLASS-THEOREM
COMPLETE CLASS-THEOREM
n.
One of the sections into which a church or congregation is divided, and which is under the supervision of a class leader.
v. t.
Anything made of glass.
n.
To arrange in classes; to classify or refer to some class; as, to class words or passages.
a.
Of the rank or degree below the best highest; inferior; second-rate; as, a second-class house; a second-class passage.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
adv.
In a complete manner; fully.
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
a.
Incomplete.
n.
To divide into classes, as students; to form into, or place in, a class or classes.
v. t.
To shut or fasten together with, or as with, a clasp; to shut or fasten (a clasp, or that which fastens with a clasp).
imp. & p. p.
of Compete
a.
Making complete.
v. t.
A looking-glass; a mirror.
n.
A group of individuals ranked together as possessing common characteristics; as, the different classes of society; the educated class; the lower classes.
v. t.
Variant of Clasp
a.
Complex, complicated.
v. t.
To case in glass.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
imp. & p. p.
of Complete