Definition:Theory/Set of Formulas

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.

Also see

• Theory of Set of Formulas is Theory