User:IssaRice/Computability and logic/Gödel's completeness theorem

semantic completeness

I'm confused about the following framing: "The completeness theorem says that, if a bunch of sentences is consistent in the sense of not entailing a contradiction [in a standard system of first-order logic] then it has a model."

if $\Gamma \models \phi$ then $\Gamma \vdash \phi$