# add axiom in a sentence

1) One can

**add**further

**axioms**restricting the dimension or the coordinate ring.

2)

**adding**

**axioms**to "K" gives rise to other well-known modal systems.

axiom collocations

3) This approach also

**adds**certain

**axioms**about equality to the deductive system employed.

4) When this

**axiom**is

**added**to RCA0, the resulting subsystem is called WKL0.

## add axiom example sentences

5) The standard response to this mismatch of prediction and observation is to**add**various psychological

**axioms**to the game-theoretic framework.

6) Next he proved that if this weaker system is consistent, it remains consistent after

**adding**the

**axiom**of regularity.

7) Stronger systems of modal logic (named S4, S5, and Brouwerian) can be obtained by

**adding**

**axioms**that the modality of a proposition is itself a necessary modal truth.

8) Unlike the situation with hyperbolic geometry, where we just

**add**one new axiom, we can not obtain a consistent system by

**adding**this statement as a new

**axiom**to the

**axioms**of absolute geometry.

9) 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.

10) They are not shown in the Metamath Proof Explorer because they have been developed by

**adding**extra

**axioms**to the standard

**axioms**of "set.mm".

11) Hilbert 1927:467

**adds**only two

**axioms**of equality, the first is x = x, the second is (x = y) → ((f(x) → f(y)); the "for all f" is missing (or implied).

12) A finer Curry–Howard correspondence exists for classical logic if one defines classical logic not by

**adding**an

**axiom**such as Peirce's law, but by allowing several conclusions in sequents.

13) If one tries to "

**add**the missing

**axioms**" to avoid the incompleteness of the system, then one has to

**add**either "p" or "not "p"" as

**axioms**.

14) If an

**axiom**is ever

**added**that makes the system complete, it does so at the cost of making the system inconsistent.

### example sentences with axiom

15) One introduces into the single-sorted theory a unary predicate symbol for each sort in the many-sorted theory, and**adds**an

**axiom**saying that these unary predicates partition the domain of discourse.

16) This change requires

**adding**additional

**axioms**to the theory at hand, so that interpretations of the predicate symbols used have the correct semantics.

17) The assumption that ZF is consistent is harmless because

**adding**another

**axiom**to an already inconsistent system cannot make the situation worse.

18) The following

**axiom**is

**added**to turn ZF into ZFC:

19) The extension to either Euclidean or Minkowskian geometry is achieved by

**adding**various further

**axioms**of orthogonality, etc

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