[permalink] [id link]

Every first-order formula is logically equivalent ( in classical logic ) to some formula in prenex normal form.

from
Wikipedia

## Some Related Sentences

Every and first-order

__Every__

__first-order__

**formula**can be converted into Skolem

**normal**

**form**while not changing its satisfiability via a process called Skolemization

**(**sometimes spelled " Skolemnization ").

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 is

__Every__legislator from Brasstown Bald

**to**Folkston

__is__going

**to**have his every vote subjected

**to**the closest scrutiny as a test of his political allegiances, not his convictions

**.**

__Every__detail

**in**his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings

**to**the fifth variation

**(**an obvious indication that he

__is__playing with Viennese musicians

**)**, and the gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics

**.**

__Every__few days,

**in**the early morning, as the work progressed, twenty men would appear

**to**push it ahead and

**to**shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it

__is__by ancient brick vaulting

**.**

__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__library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it

__is__

**to**hear the librarian say apologetically, `` I'm sorry, but we don't have that book

**.**

__Every__community, if it

__is__alive has a spirit, and that spirit

__is__the center of its unity and identity

**.**

The restricted principle "

__Every__partially ordered set has a maximal totally ordered subset "__is__also**equivalent****to**AC over ZF**.**__Every__natural-born citizen of a foreign state who

__is__also an American citizen and every natural-born American citizen who

__is__a citizen of a foreign land owes a double allegiance, one

**to**the United States, and one

**to**his homeland

**(**

**in**the event of an immigrant becoming a citizen of the US ), or

**to**his adopted land

**(**

**in**the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

__Every__line of written text

__is__a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text

__is__a tissue of quotations drawn from the innumerable centres of culture "; it

__is__never original

**.**

__Every__year, on the last Sunday

**in**April, there

__is__an ice fishing competition

**in**the frozen estuarine waters of the Anadyr River's mouth

**.**

__Every__lattice element of the structure

__is__

**in**its proper place, whether it

__is__a single atom or a molecular grouping

**.**

Every and logically

#

__Every__plurality, being a combination of units, presupposes an original unity ; hence, even those that assume a plurality of gods must__logically__admit the prior existence of a Divine Unity — a Neoplatonic argument borrowed by Baḥya from the Brothers of Purity**.**

Every and equivalent

*

__Every__quadratic Bézier curve**is**also a cubic Bézier curve, and more generally, every degree n Bézier curve**is**also a degree m curve for any m > n**.**In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub >**is**__equivalent__**(**including the parametrization**)****to**the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where**.**__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__question and method about differential equations has a discrete

__equivalent__for difference equations

**.**

__Every__Dean of the Faculty

**(**

__equivalent__

**to**a Provost at most universities

**)**has always been an active-duty brigadier general, although technically, a civilian may hold the position

**.**

__Every__homeomorphism

**is**a homotopy equivalence, but the converse

**is**not true: for example, a solid disk

**is**not homeomorphic

**to**a single point, although the disk and the point are homotopy

__equivalent__

**.**

__Every__quadratic

**form**q

**in**n variables over a field of characteristic not equal

**to**2

**is**

__equivalent__

**to**a diagonal

**form**

__Every__Riemann surface

**is**the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering

**is**holomorphically isomorphic

**(**one also says: " conformally

__equivalent__")

**to**one of the following:

__Every__year on the

__equivalent__date

**to**the 23rd of March on the Chinese Calendar, the birthday of Mazu

**is**commemorated with concerts, lion dance, Carrying god ride ' Kheng kiu ', ' siam hee ' and also wayang kulit show for three days

**.**

__Every__year, a volume of over 2 million forty-foot

__equivalent__units

**(**FEU

**)**

**is**transported worldwide

**.**

__Every__year during this period, more than a hundred MBA students from IIM Calcutta leave for foreign institutes, and an

__equivalent__number from various B-schools arrive

**in**IIM Calcutta

**to**spend the term there

**.**

__Every__CW-complex possesses a Postnikov tower, that

**is**, it

**is**homotopy

__equivalent__

**to**an iterated fibration with fibers the Eilenberg – MacLane spaces

**.**

__Every__man had

**to**go

**to**church once a week or be fined 12 pence

**(**

__equivalent__

**to**just over £ 11

**in**2007 ), a considerable sum for the poor

**.**

__Every__Toontask has an award for completion, such as additional " laff points "

**(**

__equivalent__

**to**the player's " health "), jellybeans

**(**the in-game currency ), and a variety of other benefits

**.**

*

__Every__time a loan balance**is**reduced, an__equivalent__number of bonds are identified by lottery and converted into a different bond also with a one cent par value**(**that will convert at par into cash at the next payment date ).0.578 seconds.