Definition:Independent Axiom

Definition

Let $\FF$ be a formal (logical) system.

Let $\AA$ be an axiom of $\FF$.

Then $\AA$ is independent if and only if $\AA$ is not a formal consequence of any other axioms of $\FF$.

Also see

• Results about independent axioms can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): independent: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): independent: 1.