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Completeness of first-order logic was first explicitly established by Gödel, though some of the main results were contained in earlier work of Skolem.

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## Some Related Sentences

Completeness and first-order

The

__Completeness__theorem establishes an equivalence**in**__first-order__**logic****,**between**the**formal provability**of**a formula**,**and its truth**in**all possible models**.**

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 was

A treatise entitled The Atonement ; its Reality

**,**__Completeness__and Extent ( 1861 )__was__based upon a smaller**work**which**first**appeared**in**1845**.**
This

__was__quickly followed**by**a French translation**,****in**which Hilbert added V**.**2**,****the**__Completeness__Axiom**.**

Completeness and by

__Completeness__and accuracy is described

__by__

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

**the**accuracy

**of**

**the**positions

**.**

*

__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**.**
#

__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**.**
Tsogyel

**,****though**fairly obviously a transformation**of**an older Bön figure**,**Bönmo Tso ( female Bön practitioner**of****the**lake ), whom she debates**in**her " autobiography ", also preserves**the**Great__Completeness__traditions shared__by__Bön with Tibet's earliest Buddhist tradition**.**

Completeness and Gödel

" 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 and some

__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

**.**

*

__Completeness__: If x ∈ L then for__some__π**,**V < sup > π </ sup >( x ) accepts with probability at least c ( n ),

Completeness and were

Five singles

__were__released from Thirsty Merc: " Emancipate Myself ", " My__Completeness__", " Someday**,**Someday ", " In**the**Summertime ", and " When**the**Weather Is Fine ".
*

__Completeness__checks-controls that ensure all records__were__processed from initiation to completion**.**

Completeness and .

__Completeness__and accuracy

**of**recall

**in**

**the**diffusion

**of**

**the**news from a newspaper vs a television source

__.__

The word Dzogchen has been translated variously as Great Perfection

**,**Great__Completeness__**,**Total__Completeness__**,**and Supercompleteness__.__
* (

__Completeness__) Every universally valid second-order formula**,**under standard semantics**,**is provable__.____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__.__

first-order and logic

** If S is a set

**of**sentences**of**__first-order____logic__and B is a consistent subset**of**S**,**then B is included**in**a set that is maximal among consistent subsets**of**S**.**The special case where S is**the**set**of**all__first-order__sentences**in**a given signature is weaker**,**equivalent to**the**Boolean prime ideal theorem ; see**the**section " Weaker forms " below**.**
** Gödel's completeness theorem for

__first-order____logic__: every consistent set**of**__first-order__sentences has a completion**.**
The Löwenheim-Skolem theorems tell us that if we restrict ourselves to

__first-order____logic__**,**any axiom system for**the**reals admits other models**,**including both models that are smaller than**the**reals and models that are larger**.**
In contrast

**,**other**,**more systematic algorithms achieved**,**at least theoretically**,**completeness for__first-order____logic__**.**
A basic objective

**of****the****first**normal form defined**by**Codd**in**1970**was**to permit data to be queried and manipulated using a " universal data sub-language " grounded**in**__first-order____logic__**.**
Properties definable

**in**__first-order____logic__that an equivalence relation may or may not possess include:
* Tarski's axioms: Alfred Tarski ( 1902 – 1983 ) and his students defined elementary Euclidean geometry as

**the**geometry that can be expressed**in**__first-order____logic__and does not depend on set theory for its logical basis**,****in**contrast to Hilbert's axioms**,**which involve point sets**.**
The asks for an algorithm that takes as input a statement

**of**a__first-order____logic__( possibly with a finite number**of**axioms beyond**the**usual axioms**of**__first-order____logic__) and answers " Yes " or " No " according to whether**the**statement is universally valid**,**i**.**e., valid**in**every structure satisfying**the**axioms**.**
By

**the**completeness theorem**of**__first-order____logic__**,**a statement is universally valid if and only if it can be deduced from**the**axioms**,**so**the**can also be viewed as asking for an algorithm to decide whether a given statement is provable from**the**axioms using**the**rules**of**__logic__**.**
Alphabets can also be infinite ; e

**.**g**.**__first-order____logic__is often expressed using an alphabet which**,**besides symbols such as ∧, ¬, ∀ and parentheses**,**contains infinitely many elements x < sub > 0 </ sub >, x < sub > 1 </ sub >, x < sub > 2 </ sub >, … that play**the**role**of**variables**.**
It is also known as

__first-order__predicate calculus**,****the**lower predicate calculus**,**quantification theory**,**and predicate__logic__( a less precise term ).
A theory about

**some**topic is usually__first-order____logic__together with: a specified domain**of**discourse over which**the**quantified variables range**,**finitely many functions which map from that domain into it**,**finitely many predicates defined on that domain**,**and a recursive set**of**axioms which are believed to hold for those things**.**
Sometimes " theory " is understood

**in**a more formal sense**,**which is just a set**of**sentences**in**__first-order____logic__**.**
The adjective "

__first-order__" distinguishes__first-order____logic__from higher-order__logic__**in**which there are predicates having predicates or functions as arguments**,**or**in**which one or both**of**predicate quantifiers or function quantifiers are permitted**.**
There are many deductive systems for

__first-order____logic__that are sound ( all provable statements are true ) and complete ( all true statements are provable ).0.114 seconds.