Page "Axiom" Paragraph 1

Non-logical axioms are often simply referred to as axioms in mathematical discourse.

This does not mean that it is claimed that they are true in some absolute sense.

For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.