Category:Logical Consistency
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This category contains results about Logical Consistency.
Definitions specific to this category can be found in Definitions/Logical Consistency.
Let $\LL$ be a logical language.
Let $\mathscr P$ be a proof system for $\LL$.
Proof System
Then $\mathscr P$ is consistent if and only if:
- There exists a logical formula $\phi$ such that $\not \vdash_{\mathscr P} \phi$
That is, some logical formula $\phi$ is not a theorem of $\mathscr P$.
Set of Formulas
Let $\FF$ be a collection of logical formulas.
Then $\FF$ is consistent for $\mathscr P$ if and only if:
- There exists a logical formula $\phi$ such that $\FF \nvdash_{\mathscr P} \phi$.
That is, some logical formula $\phi$ is not a provable consequence of $\FF$.
Subcategories
This category has only the following subcategory.
Pages in category "Logical Consistency"
The following 4 pages are in this category, out of 4 total.