# 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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