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The Completeness theorem establishes an equivalence in first-order logic, between the formal provability of a formula, and its truth in all possible models.

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## Some Related Sentences

Completeness and theorem

* MPC Java-based implementation A Java-based implementation

**of****the**MPC protocol based on Michael**.**B**,**Shafi**.**G**and**Avi**.**W's__theorem__("__Completeness__theorems for non-cryptographic fault-tolerant distributed computation ") with Welch-Berlekamp error correcting code algorithm to BCH codes**.**

Completeness and first-order

__Completeness__

**of**

__first-order__

**logic**was first explicitly established by Gödel

**,**though some

**of**

**the**main results were contained

**in**earlier work

**of**Skolem

**.**

Completeness and logic

Two

**of**Kripke's earlier works**,**A__Completeness__Theorem**in**Modal Logic**and**Semantical Considerations on Modal Logic**,****the**former written while he was still**a**teenager**,**were on**the**subject**of**modal__logic__**.**
* Zach

**,**Richard**,**( 1999 ), "__Completeness__before Post: Bernays**,**Hilbert**,****and****the**development**of**propositional__logic__", Bulletin**of**Symbolic Logic**,**5 ( 3 ): 331-366**.**

Completeness and between

*

__Completeness__–**all**actions can be ranked**in****an**order**of**preference ( indifference__between__two or more is**possible**).

Completeness and formula

* (

__Completeness__) Every universally valid second-order__formula__**,**under standard semantics**,**is provable**.**

Completeness and its

__Completeness__seems to be at

**the**center

**of**shalom as we will see

**in**

**the**meaning

**of**

**the**term itself

**,**

**in**some derivatives from

__its__root

**,**shalam

**,**

**in**some examples

**of**

__its__uses

**in**Jewish

**and**Christian Scriptures

**,**

**and**

**in**some homophone terms from other Semitic languages

**.**

A treatise entitled

**The**Atonement ;__its__Reality**,**__Completeness__**and**Extent ( 1861 ) was based upon**a**smaller work which first appeared**in**1845**.**
It says that one who hears

__its__reading will attain Ultimate__Completeness__**,****and**one who abuses it will be sentenced to Hell**.**

Completeness and all

*

__Completeness__;**the**degree to which__all__necessary concepts**of****the**application domain are represented**in****the**way**of**modeling**.**
*

__Completeness__checks-controls that ensure__all__records were processed from initiation to completion**.**

Completeness and possible

__Completeness__

**of**

**the**market is also important because

**in**

**an**incomplete market there are

**a**multitude

**of**

__possible__prices for

**an**asset corresponding to different risk-neutral measures

**.**

"

**The**Gelukpa allow that it is__possible__to take**the**mind itself as**the**object**of**meditation**,**however**,**Zahler reports**,****the**Gelukpa discourage it with " what seems to be thinly disguised sectarian polemics against**the**Nyingma Great__Completeness__**and**Kagyu Great Seal meditations**.**

Completeness and models

Completeness and .

__Completeness__

**and**accuracy is described by

**the**weakest apparent magnitude V ( largest number )

**and**

**the**accuracy

**of**

**the**positions

__.__

__Completeness__

**and**accuracy

**of**recall

**in**

**the**diffusion

**of**

**the**news from

**a**newspaper vs

**a**television source

__.__

" Another Approach:

**The**Church-Turing ' Thesis ' as**a**Special Corollary**of**Gödel's__Completeness__Theorem ,"**in**Computability: Gödel**,**Turing**,**Church**,****and**beyond**,**Copeland**,**B__.__J., Posy**,**C.,**and**Shagrir**,**O__.__
*

__Completeness__: if**the**statement is true**,****the**honest verifier ( that is**,**one following**the**protocol properly ) will be convinced**of**this fact by**an**honest prover__.__**The**word Dzogchen has been translated variously as Great Perfection

**,**Great

__Completeness__

**,**Total

__Completeness__

**,**

**and**Supercompleteness

__.__

theorem and establishes

Gödel's completeness

__theorem____establishes__**the**completeness**of****a**certain commonly used type**of**deductive system**.**
Gödel's completeness

__theorem__is**a**fundamental__theorem__**in**mathematical**logic**that__establishes__**a**correspondence**between**semantic**truth****and**syntactic**provability****in****first-order****logic****.****The**most fundamental results

**of**this theory are Shannon's source coding

__theorem__

**,**which

__establishes__that

**,**on average

**,**

**the**number

**of**bits needed to represent

**the**result

**of**

**an**uncertain event is given by

**its**entropy ;

**and**Shannon's noisy-channel coding

__theorem__

**,**which states that reliable communication is

**possible**over noisy channels provided that

**the**rate

**of**communication is below

**a**certain threshold

**,**called

**the**channel capacity

**.**

**The**fundamental

__theorem__

**of**arithmetic

__establishes__

**the**central role

**of**primes

**in**number theory: any integer greater than 1 can be expressed as

**a**product

**of**primes that is unique up to ordering

**.**

This

__theorem____establishes__**an**important connection**between****a**Hilbert space**and****its**( continuous ) dual space: if**the**underlying field is**the**real numbers**,****the**two are isometrically isomorphic ; if**the**field is**the**complex numbers**,****the**two are isometrically anti-isomorphic**.**
Lagrange's four-square

__theorem__**of**1770 states that every natural number is**the**sum**of**at most four squares ; since three squares are not enough**,**this__theorem____establishes__g ( 2 ) = 4**.**
Moreover

**,**if**the**relation '≥'**in****the**above expression is actually**an**equality**,**then**and**hence ;**the**definition**of**z then__establishes__**a**relation**of**linear dependence**between**u**and**v**.**This__establishes__**the**__theorem__**.**
By induction

**,**Hilbert's basis__theorem____establishes__that**,****the**ring**of****all**polynomials**in**n variables with coefficients**in****,**is**a**Noetherian ring**.**
* 1854 – Clausius

__establishes__**the**importance**of**dQ / T ( Clausius's__theorem__), but does not yet name**the**quantity**.****The**

__theorem__

__establishes__Shannon's channel capacity for such

**a**communication link

**,**

**a**bound on

**the**maximum amount

**of**error-free digital data ( that is

**,**information ) that can be transmitted with

**a**specified bandwidth

**in**

**the**presence

**of**

**the**noise interference

**,**assuming that

**the**signal power is bounded

**,**

**and**that

**the**Gaussian noise process is characterized by

**a**known power or power spectral density

**.**

Shannon's

__theorem__shows how to compute**a**channel capacity from**a**statistical description**of****a**channel**,****and**__establishes__that given**a**noisy channel with capacity C**and**information transmitted at**a**line rate R**,**then if
Hilbert's Nullstellensatz ( German for "

__theorem__**of**zeros ," or more literally**,**" zero-locus-theorem " – see Satz ) is**a**__theorem__which__establishes__**a**fundamental relationship**between**geometry**and**algebra**.**
One can prove

**the**compactness__theorem__using Gödel's completeness__theorem__**,**which__establishes__that**a**set**of**sentences is satisfiable if**and**only if no contradiction can be proven from it**.****The**recursion

__theorem__

__establishes__

**the**existence

**of**such

**a**fixed point

**,**assuming that F is computable

**,**

**and**is sometimes called ( Kleene's ) fixed point

__theorem__for this reason

**.**

Gödel's second incompleteness

__theorem____establishes__that logical systems**of**arithmetic can never contain**a**valid proof**of**their own consistency**.**
Post's

__theorem____establishes__**a**close connection**between****the**arithmetical hierarchy**of**sets**of**natural numbers**and****the**Turing degrees**.**
* 1977: D

**.**Sullivan__establishes__his__theorem__on**the**existence**and**uniqueness**of**Lipschitz**and**quasiconformal structures on topological manifolds**of**dimension different from 4**.**0.229 seconds.