Definition:Independent Proof System

Definition

Let $\mathcal L$ 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. 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