# additional axiom in a sentence

1) The final step derived Einstein's equations from the weakest possible set of additional axioms.

2) A topos can also be considered as a specific type of category with two additional topos axioms.

axiom collocations
3) This relationship between physical measurements and Hilbert space operators is, for standard quantum mechanics, an additional axiom of the theory.

4) In the axiomatic approach to hyperbolic geometry (also referred to as Lobachevskian geometry or Bolyai–Lobachevskian geometry), one additional axiom is added to the axioms giving absolute geometry.

## additional axiom example sentences

5) To supplement the four (down from five; see Post) axioms of the propositional calculus, Gödel 1930 adds the "dictum de omni" as the first of two additional axioms.

6) This first half of this axiom -- "the maxim of all" will appear as the first of two additional axioms in Gödel's axiom set.

7) We shall define a polytope, then, as a set of faces P with an order relation, and which satisfies certain additional axioms.

8) Although the structure of "L" is more regular and well behaved than that of "V", few mathematicians argue that "V" = "L" should be added to ZFC as an additional axiom.

9) It is possible to define a larger theory "T'" that contains the whole of "T", plus "G" as an additional axiom.

10) Many properties of Borel sets can be established in ZFC, but proving these properties hold for more complicated sets requires additional axioms related to determinacy and large cardinals.

11) These axioms, together with the additional axiom of replacement proposed by Abraham Fraenkel, are now called Zermelo–Fraenkel set theory (ZF).

12) In a FOL system additional axioms are required to infer facts such as a block does not change position unless it is moved.

13) This change requires adding additional axioms to the theory at hand, so that interpretations of the predicate symbols used have the correct semantics.

14) In that case one needs additional axioms that specify how much memory each ADT instance uses, as a function of its state, and how much of it is returned to the pool by __CODE__.

### example sentences with axiom

15) These axiom schemata are also used in the predicate calculus, but additional logical axioms are needed to include a quantifier in the calculus.

16) Two additional axioms have since been added to the theory:

17) Classical logic extends intuitionistic logic with an additional axiom or principle of excluded middle:

18) __FORMULA__ has a primitive concept of quasi-cardinal, governed by eight additional axioms, intuitively standing for the quantity of objects in a collection.

19) "Inaccessible cardinals yield models of ZF and sometimes additional axioms, and are equivalent to the existence of the Grothendieck universe set"

20) An axiomatic treatment of plane affine geometry can be built from the axioms of ordered geometry by the addition of two additional axioms:

21) In theory, many other abstract data structures can be viewed as set structures with additional operations and/or additional axioms imposed on the standard operations.

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