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Topics referred to by the same term
Finite completeness may refer to: Complete category, a category in which all finite limits exist Completeness (order theory)#Finite completeness, a condition
Finite_completeness
Existence of certain infima or suprema of a given poset
notion of bounded completeness given below. Further simple completeness conditions arise from the consideration of all non-empty finite sets. An order in
Completeness_(order_theory)
Category in which all small limits exist
completeness is that of finite completeness. A category is finitely complete if all finite limits exists (i.e. limits of diagrams indexed by a finite
Complete_category
Partially ordered set in which all subsets have both a supremum and infimum
supremum and an infimum. Every non-empty finite lattice is complete, but infinite lattices may be incomplete. Complete lattices appear in many applications
Complete_lattice
Fundamental theorem in mathematical logic
Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is soundness, the fact that only logically
Gödel's_completeness_theorem
Ability of a computing system to simulate Turing machines
able to recognize or decode other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule
Turing_completeness
Finite-state machine
deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state
Deterministic finite automaton
Deterministic_finite_automaton
Branch of logic
model theory that fail for finite structures under finite model theory include the compactness theorem, Gödel's completeness theorem, and the method of
Finite_model_theory
Characteristic of some logical systems
syntactically complete. Syntactical completeness can also refer to another unrelated concept, also called Post completeness or Hilbert–Post completeness. In this
Completeness_(logic)
Mathematical model of computation
theoretical computer science, a finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine
Finite-state_machine
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Attempt to formalize all of mathematics, based on a finite set of axioms
possible to prove forms of completeness for many other interesting systems. An example of a non-trivial theory for which completeness has been proved is the
Hilbert's_program
Computation model defining an abstract machine
into discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that
Turing_machine
Theorem classifying finite simple groups
classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every finite simple group is either
Classification of finite simple groups
Classification_of_finite_simple_groups
Area of mathematical logic
trivial, since every proof can have only a finite number of antecedents used in the proof. The completeness theorem allows us to transfer this to satisfiability
Model_theory
Mathematical group based upon a finite number of elements
In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical
Finite_group
Form of logic that allows quantification over predicates
hypothesis does not hold. This theory consists of a finite theory characterizing the real numbers as a complete Archimedean ordered field plus an axiom saying
Second-order_logic
Discrete analog of a derivative
A finite difference is a mathematical expression of the form f(x + b) − f(x + a). Finite differences (or the associated difference quotients) are often
Finite_difference
Algebraic structure
a finite field or Galois field (so-named in honor of Évariste Galois) is a field that has a finite number of elements. As with any field, a finite field
Finite_field
Order whose elements are all comparable
the completeness of X: If the order topology on X is connected, X is complete. X is connected under the order topology if and only if it is complete and
Total_order
Concept in mathematical logic
adequate. From the point of view of digital electronics, functional completeness means that every possible logic gate can be realized as a network of
Functional_completeness
Statistics term
In statistics, completeness is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. It is opposed to
Completeness_(statistics)
Number representing a continuous quantity
structures have a notion of completeness; the description in § Completeness is a special case. (We refer to the notion of completeness in uniform spaces rather
Real_number
Unsolved problem in computer science
many equivalent ways of describing NP-completeness. Let L be a language over a finite alphabet Σ. L is NP-complete if, and only if, the following two conditions
P_versus_NP_problem
State of being limited or ended
Finiteness, finitude, or being finite, is the state of being limited or having an end, and is a counter to the concept of infinity. Humans are considered
Finiteness
Whether a decision problem has an effective method to derive the answer
system, especially in the context of first-order logic where Gödel's completeness theorem establishes the equivalence of semantic and syntactic consequence
Decidability_(logic)
Mathematics of real numbers and real functions
from the rational numbers by their completeness. Roughly speaking, the real numbers have no gaps. This completeness can be formalized in several equivalent
Real_analysis
theorem implies that Gödel's completeness theorem (that is fundamental to first-order logic) does not hold in the finite case. Also it seems counter-intuitive
Trakhtenbrot's_theorem
Impossible task in computing
proven 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
Entscheidungsproblem
Theorem in mathematical logic
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 tool in model theory
Compactness_theorem
Existence of values making formula true
model if and only if it has a finite model. This question is important in the mathematical field of finite model theory. Finite satisfiability and satisfiability
Satisfiability
Axiom of set theory
II-finite, III-finite, IV-finite, V-finite, VI-finite and VII-finite. I-finiteness is the same as normal finiteness. IV-finiteness is the same as Dedekind-finiteness
Axiom_of_choice
Commutative group (mathematics)
groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. An abelian
Abelian_group
Group without normal subgroups other than the trivial group and itself
for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple
Simple_group
as the "content completeness problem". The problem stems from the greater expressiveness of natural language relative to the finite enumeration of concepts
Content_completeness_problem
Study of discrete mathematical structures
can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deal with finite sets, particularly
Discrete_mathematics
Type of finite-state machine in automata theory
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its
Nondeterministic finite automaton
Nondeterministic_finite_automaton
Finite collection of distinct objects
In mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically
Finite_set
Mathematical proposition equivalent to the axiom of choice
tell about Zorn's lemma?" Zorn's lemma is also equivalent to the strong completeness theorem of first-order logic. Moreover, Zorn's lemma (or one of its equivalent
Zorn's_lemma
Concept in logic
theory, a finite game (sometimes called a founded game or a well-founded game) is a two-player game that is assured to end after a finite number of moves
Finite_game
Complexity class used to classify decision problems
ISBN 0-534-94728-X. Sections 7.3–7.5 (The Class NP, NP-completeness, Additional NP-complete Problems), pp. 241–271. David Harel, Yishai Feldman. Algorithmics:
NP_(complexity)
Type of vector space in math
Kainth (2023). For the completeness of Euclidean space, see Definition 4.37 and Example 4.38, p. 108; for the equivalence of completeness with the property
Hilbert_space
Non-contradiction of a theory
in a particular deductive logic, the logic is called complete.[citation needed] The completeness of the propositional calculus was proved by Paul Bernays
Consistency
Well-quasi-ordering of finite trees
In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic
Kruskal's_tree_theorem
Consistency of the axioms of arithmetic
but a stronger system with a second-order completeness axiom. The system Hilbert asked for a completeness proof of is more like second-order arithmetic
Hilbert's_second_problem
Formal semantics for non-classical logic systems
corresponding class of L than to prove its completeness, thus correspondence serves as a guide to completeness proofs. Correspondence is also used to show
Kripke_semantics
Philosophy of mathematics that accepts the existence only of finite mathematical objects
not cause a problem regarding finite objects. This led to Hilbert's program of proving both consistency and completeness of set theory using finitistic
Finitism
Sequence of points that get progressively closer to each other
progresses. More precisely, given any small positive distance, all excluding a finite number of elements of the sequence are less than that given distance from
Cauchy_sequence
Infinite cardinal number
_{0}} : Every finite set of natural numbers has a maximum, which is also a natural number, and finite unions of finite sets are finite. An example application
Aleph_number
Set of functions used to represent the electronic wave function
Vaara have proposed completeness-optimized basis sets, where the exponents are obtained by maximization of the one-electron completeness profile instead of
Basis_set_(chemistry)
Generalization of the discrete Fourier transform
the Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform
Fourier transform on finite groups
Fourier_transform_on_finite_groups
Model of computation over real numbers
Quantum finite automaton Blum, Lenore; Shub, Mike; Smale, Steve (1989). "On a Theory of Computation and Complexity over the Real Numbers: NP-completeness, Recursive
Blum–Shub–Smale_machine
Size of a possibly infinite set
(bijection) between the elements of the two sets. The cardinality of a finite set can be identified with a natural number, which can be found simply by
Cardinal_number
Subfield of mathematics
proved the completeness theorem, which establishes a correspondence between syntax and semantics in first-order logic. Gödel used the completeness theorem
Mathematical_logic
When a finite set S of relations yields polynomial-time or NP-complete problems
sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of
Schaefer's_dichotomy_theorem
American philosopher and logician (1940–2022)
use FMP to prove Kripke completeness of a logic: every normal modal logic is complete wrt a class of modal algebras, and a finite modal algebra can be transformed
Saul_Kripke
Collection of mathematical objects
{\displaystyle \emptyset } ) and the latter has no elements at all. A set is finite if there exists a natural number n {\displaystyle n} such that the first
Set_(mathematics)
≥ | σ | {\displaystyle \kappa \geq |\sigma |} and has no finite model, then it is complete. This theorem was proved independently by Jerzy Łoś (1954)
Łoś–Vaught_test
Theories in mathematical logic
properties: it is complete, decidable, finitely axiomatizable, and so on. The only problem is that it has no models at all. By Gödel's completeness theorem, it
List_of_first-order_theories
Verb form that can complete an independent clause by itself
English imperative). A finite transitive verb or a finite intransitive verb can function as the root of an independent clause. Finite verbs are distinguished
Finite_verb
Partial order with joins
partially ordered set that has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice (or lower semilattice) is a partially
Semilattice
Template that specifies one or more axioms
is an instance of the schema. Axiom schemata are commonly used to give finite descriptions of theories whose axioms include infinitely many formulas.
Axiom_schema
Benjamin (2013). "Godel's Completeness Theorem and Deligne's Theorem". arXiv:1309.0389 [math.LO]. "Deligne completeness theorem". nLab. Grothendieck
Coherent_topos
In logic, a statement which is always true
the task of determining whether or not the formula is a tautology is a finite and mechanical one: one needs only to evaluate the truth value of the formula
Tautology_(logic)
Study of the properties of logical systems
1920) Completeness of first-order monadic predicate logic (Leopold Löwenheim 1915) Completeness of first-order predicate logic (Gödel's completeness theorem
Metalogic
Mathematical model describing how an output of a function is computed given an input
models, functional models, and concurrent models. Sequential models include: Finite-state machines Post machines (Post–Turing machines and tag machines). Pushdown
Model_of_computation
PSPACE-complete". Theoretical Computer Science. 123 (2): 329–340. doi:10.1016/0304-3975(94)90131-7. Hearn; Demaine (2002). "PSPACE-Completeness of Sliding-Block
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
Limitative results in mathematical logic
with semantic completeness, which means that the set of axioms proves all the semantic tautologies of the given language. In his completeness theorem (not
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Algebraic structure with an associative operation and an identity element
monoid. Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for
Monoid
Ordered listing of items in collection
elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set. There
Enumeration
System of formal deduction in logic
systems, additionally require the necessitation rule. Some systems use a finite list of concrete formulas as axioms instead of an infinite set of formulas
Hilbert_system
Set of sentences in a formal language
For 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)
Model of (first-order) Peano arithmetic that contains non-standard numbers
arithmetic, is neither provable nor disprovable in Peano arithmetic. By the completeness theorem, this means that G is false in some model of Peano arithmetic
Non-standard model of arithmetic
Non-standard_model_of_arithmetic
Representations of finite groups, particularly on vector spaces
on permutation representations. Other than a few marked exceptions, only finite groups will be considered in this article. We will also restrict ourselves
Representation theory of finite groups
Representation_theory_of_finite_groups
Type of theory in mathematical logic
characterizing the model's structure. In first-order logic, only theories with a finite model can be categorical, due to the upward Löwenheim–Skolem theorem. Higher-order
Categorical_theory
One-to-one correspondence
from some finite set to the first natural numbers (1, 2, 3, ...), up to the number of elements in the counted set. It results that two finite sets have
Bijection
NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states
NFA_minimization
Set of elements in any of some sets
one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set. The notation for
Union_(set_theory)
Property of a partially ordered set
property is one form of the completeness axiom for the real numbers, and is sometimes referred to as Dedekind completeness. It can be used to prove many
Least-upper-bound_property
Term in logic and deductive reasoning
special sense of completeness, in which the class of models (up to isomorphism) is restricted to the intended one. The original completeness proof applies
Soundness
Concept in mathematical logic
sense of "semantically valid"). Gödel's completeness theorem is about this latter kind of completeness. Complete theories are closed under a number of conditions
Complete_theory
Mathematical theorem
orthogonality of the system, and of the completeness of L 2 . {\displaystyle L^{2}.} Fischer's proof of completeness is somewhat indirect. It uses the fact
Riesz–Fischer_theorem
Logical principle
to the study of concrete operations on finite or potentially (but not actually) infinite structures; completed infinite totalities … were rejected, as
Law_of_excluded_middle
Numerical analysis technique
Finite-difference time-domain (FDTD) or Yee's method (named after the Chinese American applied mathematician Kane S. Yee, born 1934) is a numerical analysis
Finite-difference time-domain method
Finite-difference_time-domain_method
Statement that is taken to be true
interpretation". Gödel's completeness theorem establishes the completeness of a certain commonly used type of deductive system. Note that "completeness" has a different
Axiom
Belief in a deity that is not omnipotent
Theistic finitism, also known as finitistic theism or finite godism, is the belief in a deity that is limited. It has been proposed by some philosophers
Theistic_finitism
Process of repeating items in a self-similar way
propositions is the smallest set of propositions satisfying these conditions. Finite subdivision rules are a geometric form of recursion, which can be used to
Recursion
Problem in computer science
bounded automata (LBAs) or deterministic machines with finite memory. Such a machine has finitely many possible configurations, so any deterministic program
Halting_problem
Type of infinite structure
{\displaystyle X\subseteq M} (with parameters taken from M {\displaystyle M} ) is a finite union of intervals and points. O-minimality can be regarded as a weak form
O-minimal_theory
System of logic in mathematics and philosophy
all MV-algebras (general completeness) A {\displaystyle A} is valid in all linearly ordered MV-algebras (linear completeness) A {\displaystyle A} is valid
Łukasiewicz_logic
Manifold of dimension 3 equipped with a hyperbolic metric
discrete group of isometries (a Kleinian group). Hyperbolic 3-manifolds of finite volume have a particular importance in 3-dimensional topology as follows
Hyperbolic_3-manifold
Branch of mathematical logic
covering by a sequence of open intervals has a finite subcovering. The Heine–Borel theorem for complete totally bounded separable metric spaces (where
Reverse_mathematics
Symbolic description of a mathematical object
one. There are countably infinitely many WFE's, however, each WFE has a finite number of nodes. In computer science, an expression is a syntactic entity
Expression_(mathematics)
Type of mathematical object
general linear groups. Complete connected group schemes are in some sense opposite to affine group schemes, since the completeness implies all global sections
Group_scheme
Mathematical set of all subsets of a set
S is {{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}. If S is a finite set with the cardinality |S| = n (i.e., the number of all elements in the
Power_set
Standard system of axiomatic set theory
alone can encode the other connectives, a property known as functional completeness. This section attempts to strike a balance between simplicity and intuitiveness
Zermelo–Fraenkel_set_theory
Basic framework of mathematics
only semi-decidable as given by the completeness theorem). 1955: Pyotr Novikov showed that there exists a finitely presented group G such that the word
Foundations_of_mathematics
Formal language that can be expressed using a regular expression
be defined as a language recognised by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after
Regular_language
Computational learning model
class of finite languages is identifiable in the limit, however, this class is neither finitely nor fixed-time identifiable. Learning from complete presentation
Language identification in the limit
Language_identification_in_the_limit
Type of mathematical space
property of finite sets is that every cover of a finite set by subsets has a finite subcover: one may choose, for each point of the finite set, a member
Compact_space
FINITE COMPLETENESS
FINITE COMPLETENESS
Girl/Female
Hindu, Indian
Daughter of Mahavir Jain
Boy/Male
Hindu, Indian
Very Intelligent
Girl/Female
Tamil
Infinite, Divine
Boy/Male
Hindu
Unassuming, Knowledgeable, Modest, Venus, Requester
Girl/Female
Assamese, Bengali, Hindu, Indian, Kannada, Latin, Malayalam, Marathi, Spanish, Tamil, Telugu, Traditional
Polite Sweet; Requester Knowledge; Kindness
Girl/Female
Indian
Modest
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Modesty; Good Behaviour
Male
Portuguese
Portuguese form of Latin Philippus, FILIPE means "lover of horses."
Girl/Female
Hindu
Humble, Unassuming, Obedience, Knowledge, Venus, Requester
Girl/Female
French
May Jehovah add. Addition (to the family). A feminine form of Joseph.
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu, Traditional
Modest; The Most Lovable
Boy/Male
Hindu, Indian
Smart
Girl/Female
Indian
Infinite, Divine
Surname or Lastname
English
English : habitational name (reflecting the pronunciation of the place name) for someone from Finchale in Durham, named from Old English finc ‘finch’ + halh ‘nook or corner of land’.English : possibly a metonymic occupational name or topographic name from Middle English fenkel ‘fennel’. Compare Fennell.Respelling of German Finkel.
Boy/Male
Celtic Irish
Handsome.
Girl/Female
Hindu
Modesty, Education
Boy/Male
Indian, Telugu
Good Look
Boy/Male
Indian, Sanskrit
Decent; Domesticated
Male
English
Variant spelling of English Finnian, FINIAN means "little white one."
Boy/Male
Hindu
FINITE COMPLETENESS
FINITE COMPLETENESS
Boy/Male
Hindu, Indian
Glorious
Boy/Male
Muslim/Islamic
Leader
Male
Romanian
Romanian form of Greek Sergios, possibly SERGHEI means "sergeant."
Boy/Male
Gujarati, Hindu, Indian, Kannada
Some; One or Another
Girl/Female
Biblical
Eminences, elevations.
Female
Spanish
Feminine form of Spanish Ricardo, RICARDA means "powerful ruler." Used mostly in Germany.
Boy/Male
Muslim
Protected, Name of a companion
Girl/Female
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Goddess Laxmi
Surname or Lastname
English
English : nickname for a person believed to have supernatural qualities, from Middle English, Old French faie ‘fairy’ (Late Latin fata ‘fate’, ‘destiny’).English : nickname for a trustworthy person, from Middle English, Old French fei ‘loyalty’, ‘trust’.English (of Norman origin) and French : habitational name from any of various places in France named with Old French faie ‘beech’, or a topographic name from someone living by a beech wood. Compare Lafayette.Irish : variant of Fahey.Irish : variant of Fee.
Girl/Female
Assamese, Bengali, Hindu, Indian, Kannada, Latin, Tamil
Drawing; Painting
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
FINITE COMPLETENESS
adv.
In a finite manner or degree.
a.
Without limit in power, capacity, knowledge, or excellence; boundless; immeasurably or inconceivably great; perfect; as, the infinite wisdom and goodness of God; -- opposed to finite.
a.
Unlimited or boundless, in time or space; as, infinite duration or distance.
n.
That which is infinite; boundless space or duration; infinity; boundlessness.
n.
The Infinite Being; God; the Almighty.
a.
Of or pertaining to a minute or minutes; occurring at or marking successive minutes.
v. t.
To give occasion for; as, to invite criticism.
a.
Serving to define or restrict; limiting; determining; as, the definite article.
n.
See Conite.
n.
See Yenite.
a.
Having certain or distinct; determinate in extent or greatness; limited; fixed; as, definite dimensions; a definite measure; a definite period or interval.
v. t.
To invite or ask.
a.
To make fine; to dress finically.
a.
Attentive to small things; paying attention to details; critical; particular; precise; as, a minute observer; minute observation.
n.
An infinite quantity or magnitude.
a.
Having a limit; limited in quantity, degree, or capacity; bounded; -- opposed to infinite; as, finite number; finite existence; a finite being; a finite mind; finite duration.
n.
Fixedness; as, fixity of tenure; also, that which is fixed.
n.
The joiner work and other finer work required for the completion of a building, especially of the interior. See Inside finish, and Outside finish.
p. pr. & vb. n.
of Fine
v. t.
To kindle or set on fire; as, to ignite paper or wood.