Definition:Theory/Set of Formulas
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Definition
Let $\LL$ be a logical language.
Let $\mathscr M$ be a formal semantics for $\LL$.
Let $\FF$ be a set of $\LL$-formulas.
Then the $\LL$-theory of $\FF$, denoted $\map T {\FF}$ is the set:
- $\set {\phi \in \LL: \FF \models_{\mathscr M} \phi}$
where $\models_{\mathscr M}$ denotes $\mathscr M$-semantic consequence.