Definition:Independent Proof System

Definition

Let $\LL$ be a logical language.

Let $\mathscr P$ be a proof system.

Then $\mathscr P$ is independent if it is not possible to derive one axiom or rule of inference of $\mathscr P$ from the others.

This article is incomplete. In particular: Deliberately vague, as the context in which this definition was originally couched was equally vague. Needs to be made rigorous, or merged with pages building a more comprehensive treatment. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by expanding it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Stub}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 4.2$: The Construction of an Axiom System
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Axiom systems