# Definition:Independent Proof System

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## 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.

## 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