Definition:Absolutely Consistent Proof System

Definition

Let $\LL$ be a logical language.

Let $\mathscr P$ be a consistent proof system for $\LL$.

Then $\mathscr P$ is absolutely consistent if and only if not all WFF of $\mathscr P$ is a theorem.

Also see

• Definition:Consistent Proof System

Sources

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