Completeness Theorem for Hilbert Proof System Instance 2 and Boolean Interpretations
Jump to navigation
Jump to search
It has been suggested that this page be renamed. To discuss this page in more detail, feel free to use the talk page. |
Theorem
Instance 2 of the Hilbert proof systems is a complete proof system for boolean interpretations.
That is, for every WFF $\mathbf A$:
- $\models_{\mathrm{BI}} \mathbf A$ implies $\vdash_{\mathscr H_2} \mathbf A$
Proof
This theorem requires a proof. In particular: This is going to be fun You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. 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 {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Also see
The Soundness Theorem for Hilbert Proof System Instance 2 and Boolean Interpretations in which it is proved that:
- If $\vdash \mathbf A$ then $\models \mathbf A$.
Sources
- 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous): $\S 4.8$: Completeness: Theorem $14$