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Every first-order formula can be converted into Skolem normal form while not changing its satisfiability via a process called Skolemization ( sometimes spelled " Skolemnization ").

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## Some Related Sentences

Every and first-order

__Every__

__first-order__

**formula**is logically equivalent

**(**in classical logic ) to some

**formula**in prenex

**normal**

**form**.

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__non-trivial problem in L is complete under log-space reductions so weaker reductions are required to identify meaningful notions of L-completeness, the most common being

__first-order__reductions.

Every and formula

*

**(**Completeness )__Every__universally valid second-order__formula__, under standard semantics, is provable.__Every__once in

**a**

**while**, the column steered away from

**its**usual

__formula__to feature an issue that was

**a**current widespread issue.

__Every__arithmetical set is implicitly arithmetical ; if X is arithmetically defined by φ

**(**n ) then it is implicitly defined by the

__formula__

Every and can

__Every__such subset has

**a**smallest element, so to specify our choice function we

__can__simply say that it maps each set to the least element of that set.

__Every__information exchange between living organisms — i. e. transmission of signals that involve

**a**living sender and receiver

__can__

**be**considered

**a**

**form**of communication ; and even primitive creatures such as corals are competent to communicate.

__Every__context-sensitive grammar which does

**not**generate the empty string

__can__

**be**transformed

**into**an equivalent one in Kuroda

**normal**

**form**.

__Every__grammar in Chomsky

**normal**

**form**is context-free, and conversely, every context-free grammar

__can__

**be**transformed

**into**an equivalent one which is in Chomsky

**normal**

**form**.

__Every__module over

**a**division ring has

**a**basis ; linear maps between finite-dimensional modules over

**a**division ring

__can__

**be**described by matrices, and the Gaussian elimination algorithm remains applicable.

__Every__entire function

__can__

**be**represented as

**a**power series that converges uniformly on compact sets.

Group actions / representations:

__Every__group G__can__**be**considered as**a**category with**a**single object whose morphisms are the elements of G. A functor from G to Set is then nothing but**a**group action of G on**a**particular set, i. e.**a**G-set.__Every__sequence

__can__, thus,

**be**read in three reading frames, each of which will produce

**a**different amino acid sequence

**(**in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

__Every__hyperbola is congruent to the origin-centered East-West opening hyperbola sharing

**its**same eccentricity ε

**(**

**its**shape, or degree of

**"**spread "), and is also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that is, it

__can__

**be**rotated so that it opens in the desired direction and

__can__

**be**translated

**(**rigidly moved in the plane ) so that it is centered at the origin.

__Every__holomorphic function

__can__

**be**separated

**into**

**its**real and imaginary parts, and each of these is

**a**solution of Laplace's equation on R < sup > 2 </ sup >.

__Every__species

__can__

**be**given

**a**unique

**(**and, one hopes, stable ) name, as compared with common names that are often neither unique nor consistent from place to place and language to language.

__Every__vector v in determines

**a**linear map from R to taking 1 to v, which

__can__

**be**thought of as

**a**Lie algebra homomorphism.

__Every__use of modus tollens

__can__

**be**

**converted**to

**a**use of modus ponens and one use of transposition to the premise which is

**a**material implication.

__Every__adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and

__can__make arrangements for the care of his / her dependants during the trip, must perform the Hajj once in

**a**lifetime.

*

__Every__finite topological space gives rise to**a**preorder on**its**points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder__can__**be**formed as the specialization preorder of**a**topological space in this way.
*

__Every__preorder__can__**be**given**a**topology, the Alexandrov topology ; and indeed, every preorder on**a**set is in one-to-one correspondence with an Alexandrov topology on that set.__Every__binary relation R on

**a**set S

__can__

**be**extended to

**a**preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.

Every and be

__Every__man who dabbles in the market to make

**a**little easy money on the side and suffers losses could at the time hardly face his wife who was wondering how her husband could

__be__so dumb.

__Every__dream, and this is true of

**a**mental image of any type even though it may

__be__readily interpreted

**into**

**its**equivalent of wakeful thought, is

**a**psychic phenomenon for which no explanation is available.

__Every__Wednesday night through Oct. 11 there will

__be__an elaborate colored fountain display, with 229 nozzles throwing jets of water up to 130 feet.

__Every__time

**a**speech sound is produced for

**a**given phoneme, it will

__be__slightly different from other utterances, even for the same speaker.

* Revised Code of Washington 9. 12. 010:

**"**__Every__person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass**a**defendant in the suit, or who serves or sends any paper or document purporting to__be__or resembling**a**judicial**process**, that is**not**in fact**a**judicial**process**, is guilty of**a**misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto__be__disbarred from practicing law within this state.__Every__Hilbert space X is

**a**Banach space because, by definition,

**a**Hilbert space is complete with respect to the norm associated with

**its**inner product, where

**a**norm and an inner product are said to

__be__associated if for all x ∈ X.

__Every__person should

__be__identified uniquely as resident in one place but where they happen to

__be__on census day, their de facto residence, may

**not**

__be__the best place to count them.

__Every__adult and wise woman without husband although reserves the right to accept concubinage for her employer / master without any coercion or force, but Islamic scholars have consensus that for sex relations options of Nikkah and Muta should

__be__adopted instead of concubinage in this era.

George

__Every__claims that the existence of**"**myths in the Bible would now__be__admitted by nearly everyone ", including**"**probably all Roman Catholics and**a**majority of Protestants ".
According to

__Every__, one example may__be__**"**the myth of St. George**"**and other stories about saints battling dragons, which were**"**modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".1.126 seconds.