# satisfy axiom in a sentence

1) These meet and join operations

**satisfy**the

**axioms**defining a lattice.

2) One can check that all field

**axioms**are

**satisfied**.

axiom collocations

3) This definition of equality then automatically

**satisfies**the

**axioms**for equality.

4) A presheaf that

**satisfies**these

**axioms**is a sheaf.

## satisfy axiom example sentences

5) A closure operation**satisfying**this

**axiom**is called an "anti-exchange closure".

6) A large class of spaces

**satisfying**the countable first

**axiom**are metric spaces.

7) Such a homomorphism Δ is called a comultiplication if it

**satisfies**certain

**axioms**.

8) These models define a real hyperbolic space which

**satisfies**the

**axioms**of a hyperbolic geometry.

9) Riemann's elliptic geometry emerges as the most natural geometry

**satisfying**this axiom.

10) Thus the Stiefel–Whitney class is the unique functor

**satisfying**the four

**axioms**above.

11) Both Conway's original construction and the sign-expansion construction of surreals

**satisfy**these

**axioms**.

12) With the operations of matrix addition and matrix multiplication, this set

**satisfies**the above ring

**axioms**.

13) The association "G" __FORMULA__ is a functor (mapping between categories

**satisfying**certain

**axioms**).

14) These authors found that the

**axioms**were

**satisfied**, however, these were applications biased towards a positive result.

### example sentences with axiom

15) There are many sets that, under the operation of multiplication,**satisfy**the

**axioms**that define group structure.

16) The binary relation __FORMULA__ is a "descriptive EF-proximity", provided the following

**axioms**are

**satisfied**for __FORMULA__.

17) A structure that

**satisfies**all

**axioms**for Boolean algebras except the two distributivity

**axioms**is called an orthocomplemented lattice.

18) In dimension 2 and 3, interacting (i.e. non-free) theories which

**satisfy**the

**axioms**have been constructed.

19) The resulting structure, a model of elliptic geometry,

**satisfies**the

**axioms**of plane geometry except the parallel postulate.

20) Also, the function belongs to . One then checks that the addition and the multiplication

**satisfy**the ring

**axioms**.

21) If the collection of all covering families

**satisfies**certain

**axioms**, then we say that they form a Grothendieck pretopology.

22) The rational numbers are the smallest substructure of the real (or complex) numbers that also

**satisfies**the field

**axioms**.

23) The set N together with 0 and the successor function "s" : N → N

**satisfies**the Peano

**axioms**.

24) The resulting operations

**satisfy**the

**axioms**of a field–except that the commutativity of multiplication requires Pappus's hexagon theorem.

25) A vector space over a field __FORMULA__ is a set __FORMULA__ together with two operations that

**satisfy**the eight

**axioms**listed below.

26) Unfortunately, it proved extraordinarily difficult to show that any realistic field theory, including the Standard Model,

**satisfied**these

**axioms**.

27) All models that are isomorphic to the one just given are also called standard; these models all

**satisfy**the Peano

**axioms**.

28) In 1857, Karl von Staudt published his Algebra of Throws which provided a geometric model

**satisfying**the

**axioms**of a field.

29) See Osterwalder-Schrader theorem . This theorem is the key tool for the constructions of interacting theories in dimension 2 and 3 which

**satisfy**the Wightman

**axioms**.

30) A ring object in C is an object R equipped with morphisms (addition), (multiplication), (additive identity), (additive inverse), and (multiplicative identity)

**satisfying**the usual ring

**axioms**.

31) This means that we have a smooth multiplication μ : G × G → G, an inversion ν : G → G and a unit element e ∈ G such that the usual group

**axioms**are

**satisfied**.

32) These arguments showed that if an agent is willing to take bets on either side of any proposition, then to avoid guaranteed losses, his betting odds must

**satisfy**the standard probability

**axioms**.

33) The interesting thing to observe is that instead of having to ask, now, "Does nomological necessity

**satisfy**the

**axiom**(5)?

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