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 propositional formula can be converted into an equivalent formula that is in CNF.

* ( Completeness ) Every universally valid second-order formula, under standard semantics, is provable.

Every formula in classical logic is equivalent to a formula in prenex normal form.

Every even perfect number is hexagonal, given by the formula

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

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 single problem touched on thus far is related to good marketing planning.

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 man in every one of these houses is a Night Rider.

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 infinite game in which is a Borel subset of Baire space is determined.

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 root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

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 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 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 context-free grammar can be transformed into an equivalent pushdown automaton.

Every question and method about differential equations has a discrete equivalent for difference equations.

Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form.

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 monoidal category is monoidally equivalent to a strict monoidal category.

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 set is Turing equivalent to its complement

* 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 ).