Definition:Independent Proof System
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This article is incomplete, as follows:
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.
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.
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.
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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