Consistent Set of Formulas can be Extended to Maximal Consistent Set

Theorem

Let $\FF$ be a collection of consistent logical formulas.

Then $\FF$ can be extended to (that is, is a subset of) a maximal consistent set of formulas.

Proof

This theorem requires a proof. In particular: This is probably the same as Finitely Satisfiable Theory has Maximal Finitely Satisfiable Extension 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.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text {II}$ -- Maximal principles: $\S 5$ Maximal principles