Definition:Model (Logic)/Set of Logical Formulas

Definition

Let $\mathscr M$ be a formal semantics for a logical language $\LL$.

Let $\MM$ be a structure of $\mathscr M$.

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

Then $\MM$ is a model of $\FF$ if and only if:

$\MM \models_{\mathscr M} \phi$ for every $\phi \in \FF$

that is, if it is a model of every logical formula $\phi \in \FF$.

Also see

• Definition:Satisfiable Set of Formulas

Sources

• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\text {II}.7$ First-Order Logic Semantics: Definition $\text {II}.7.11$
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.5.2$: Definition $2.42$