Consistent Set of Logical Formulas is Subset of Maximally Consistent Set

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Theorem

Let $\LL$ be a formal language used in the field of symbolic logic.

Let $\FF$ be the set of logical formulas of $\LL$.

Let $\FF$ be countable.


Let $S$ be a consistent subset of $\FF$.

Then $S$ is a subset of some maximal consistent set of formulas.


Proof




Sources