User:IssaRice/Computability and logic/Models symbol

The "models" symbol, $\models$, is used for several purposes in mathematical logic.

• If $\mathfrak{A}$ is a structure/interpretation and $\varphi$ is a sentence, then $\mathfrak{A}\models \varphi$ means ...
• If $\mathfrak{A}$ is a structure/interpretation and $\mathrm{\Gamma }$ is a set of sentences, then $\mathfrak{A}\models \mathrm{\Gamma }$ means ...
• If $T$ is a theory and $\varphi$ is a sentence, then $T\models \varphi$ means ...
• If $T$ is a theory and $\mathrm{\Gamma }$ is a set of sentences, then $T\models \mathrm{\Gamma }$ means ...
• If $\mathrm{\Sigma }$ is a set of axioms for a theory $T$, and $\varphi$ is a sentence, then $\mathrm{\Sigma }\models \varphi$ means ...
• If $\mathrm{\Sigma }$ is a set of axioms for a theory $T$, and $\mathrm{\Gamma }$ is a set of sentences, then ...
• if $\varphi$ is a formula (or wff), then ...
• also the variant without anything in front, e.g., $\models \varphi$