: Every countable theory which is satisfiable in a model M, is satisfiable in a countable substructure of M.

Every Skolem theory is model complete, i. e. every substructure of a model is an elementary substructure.

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 elementary embedding is a strong homomorphism, and its image is an elementary substructure.

# Every elementary substructure of a model of a theory T also satisfies T ; hence it is a submodel.

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 Economic union, Customs and monetary union and Economic and monetary union has also a Customs Union

Every corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.

Every Economic union and Economic and monetary union has also a Common market

Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.

Every major rugby union touring team to visit Wales has played at Rodney Parade, and all of them were beaten at least once in the twentieth century by a side who, in 1951, played in the match at Cardiff RFC that attracted what was, a world-record crowd of 48, 500 for a rugby union match between two clubs.

* Every nonempty affine algebraic set may be written uniquely as a union of algebraic varieties ( where none of the sets in the decomposition are subsets of each other ).

Every Turán graph is a cograph ; that is, it can be formed from individual vertices by a sequence of disjoint union and complement operations.

Every cobordism is a union of elementary cobordisms, by the work of Morse, Thom and Milnor.

Note: Every cyclic permutation of definition type 3 may be seen as an union of a cyclic permutation of definition type 2 and some fixed points.

Every university has a student union ( In Danish, Studenterråd ).

Every semester, the student union organises a " 24 hour lecture ", in which many researchers of the university present interesting topics in short lectures starting at 6 pm on a Friday, and ending at 6 pm on the following Saturday.

Every closed smooth 4-manifold is a union of two Stein 4-manifolds glued along their common boundary.

Every full-time student enrolled in IUJ is automatically a member of the Graduate Student Organization ( GSO ), the students ' union of IUJ.

Every Customs and monetary union and Economic and monetary union also has a Currency Union

Every year rugby union and baseball matches Meisōsen () against Waseda University attract support among its students.

* Every worker in America has the right to a union that has the focus, strategy, and resources to unite workers in that industry and win.

Every year the world players ' union, with the help from all of its associations, distributes more than 55, 000 ballots all over the world.

Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.

Every time you transplant a pansy you cause its flowers to become smaller.

Every winter a kegful of this sauce was made and placed at the end of a row of four other kegs in the cellar, so that when its turn came, it was properly mellowed.

1 ) Every age rewrites the events of its history in terms of what should have been, creating legends about itself that rationalize contemporary beliefs and excuse contemporary actions.

Every member of the family must have a vital place in its life.

Every telephone company, whether large or small, determines its own ANAC for each individual central office, which tends to perpetuate the current situation of a mess of overlapping and / or spotty areas of coverage.

Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.

* Every collecting institution must develop an emergency plan to protect its collections and train staff to carry it out.

* Every institution must assign responsibility for caring for collections to members of its staff.

Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.

" Every performance of its run was sold out.

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 computer system provides at least one file-manager program for its native file system.

Every aspect of life was regulated to some degree by the party, and the will of its founding-president, Mobutu Sese Seko.

Every tile belongs to the two suits of its two values, e. g. 0 – 3 belongs both to the blank suit ( or 0 suit ) and to the 3 suit.

Every division ring is therefore a division algebra over its center.

Every field is, of course, one-dimensional over its center.

Every system must have a class designated as " root ", with one of its creation procedures designated as " root procedure ".

Every SE must be registered in the State where it has its registered office, in a register designated by the law of that State.

Every node on the Freenet network contributes storage space to hold files, and bandwidth that it uses to route requests from its peers.

The album's lead single, " She's Every Woman " peaked at number-one on the Billboard Country Chart, however its follow-up single, " The Fever " ( a cover of an Aerosmith song ) only peaked at number 23, becoming Brooks's first released Country single to not chart on the Top 10.