Page "Second-order logic" ¶ 29
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## Some Related Sentences

Completeness and formula
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 under
*" Tennis Player Michael Joyce's Professional Artistry as a Paradigm of Certain Stuff about Choice, Freedom, Discipline, Joy, Grotesquerie, and Human Completeness " ( Esquire, 1996, under the title " The String Theory ")

Completeness and is
* Completeness – all actions can be ranked in an order of preference ( indifference between two or more is possible ).
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 string is in the language, the prover must be able to give a certificate such that the verifier will accept with probability at least 2 / 3 ( depending on the verifier's random choices ).
# Completeness: any statement is either provable or refutable ( i. e. its negation is provable ).
; Completeness: The design must cover as many important situations as is practical.
; Completeness: The design must cover as many important situations as is practical.
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.
Completeness is a common property of market models ( for instance the Black – Scholes model ).
" 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: 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 and provable
Completeness states that all true sentences are provable.

Completeness and .
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 accuracy of recall in the diffusion of the news from a newspaper vs a television source.
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.
" A Completeness Theorem in Modal Logic ", Journal of Symbolic Logic 24 ( 1 ): 1 – 14.
" 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.
The word Dzogchen has been translated variously as Great Perfection, Great Completeness, Total Completeness, and Supercompleteness.
Completeness can be sacrificed in favor of any other quality.
* Lawrence Solum, Default Rules and Completeness, Legal Theory Lexicon.
* Lawrence Solum, Default Rules and Completeness, Legal Theory Lexicon.
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.
" The Completeness of the First-Order Functional Calculus ", Journal of Symbolic Logic.
" Completeness in the theory of types ", Journal of Symbolic Logic 15: 81 – 91.

Every and universally
* ( Soundness ) Every provable second-order sentence is universally valid, i. e., true in all domains under standard semantics.
Every analytic set is universally measurable.
* Every set of reals in L ( R ) is Lebesgue measurable ( in fact, universally measurable ) and has the property of Baire and the perfect set property.

Every and valid
: Every religion is valid and true for the time and cultural context in which it was born.
Every digit has a set of possible phonetic values, due to the variety of valid Japanese ( kun ' yomi and on ' yomi ), and English-origin pronunciations for numbers in Japanese.
* Every valid OWL Lite conclusion is a valid OWL DL conclusion.
* Every valid OWL DL conclusion is a valid OWL Full conclusion.
Every Poczta Polska office is valid target for poste restante delivery and the service is provided with no additional cost.
In Quebec, which makes use of civil law, there is a general duty to rescue in its Charter of Rights: " Every human being whose life is in peril has a right to assistance ... Every person must come to the aid of anyone whose life is in peril, either personally or calling for aid, by giving him the necessary and immediate physical assistance, unless it involves danger to himself or a third person, or he has another valid reason.

Every and second-order
For example, second-order arithmetic can express the principle " Every countable vector space has a basis " but it cannot express the principle " Every vector space has a basis ".
Many principles that imply the axiom of choice in their general form ( such as " Every vector space has a basis ") become provable in weak subsystems of second-order arithmetic when they are restricted.
Every second-order linear ODE with three regular singular points can be transformed into this equation.
Every second-order linear ODE on the extended complex plane with at most four regular singular points, such as the Lamé equation or the hypergeometric differential equation, can be transformed into this equation by a change of variable.

Every and formula
Every propositional formula can be converted into an equivalent formula that is in CNF.
Every formula in classical logic is equivalent to a formula in prenex normal form.
Every first-order formula is logically equivalent ( in classical logic ) to some formula in prenex normal form.
Every first-order formula can be converted into Skolem normal form while not changing its satisfiability via a process called Skolemization ( sometimes spelled " Skolemnization ").
Every even perfect number is hexagonal, given by the formula
A substructure N of M is elementary if and only if it passes the Tarski – Vaught test: Every first-order formula φ ( x, b < sub > 1 </ sub >, …, b < sub > n </ sub >) with parameters in N that has a solution in M also has a solution in N when evaluated in M. One can prove that two structures are elementary equivalent with the Ehrenfeucht – Fraïssé games.
Every once in a while, the column steered away from its usual formula to feature an issue that was a current widespread issue.
* Every propositional variable is a formula.
Every language has a formula for the unreal.
Every arithmetical set is implicitly arithmetical ; if X is arithmetically defined by φ ( n ) then it is implicitly defined by the formula

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