# 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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